Add logistic and Bayesian uncertainty analysis

organized_uncertainty_analysis/.gitignore

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+__pycache__/
+*.py[cod]
+.ipynb_checkpoints/
+*_executed.ipynb
+
+# Private clinical input data (results remain publishable separately)
+*.mat
+.DS_Store
+Thumbs.db

organized_uncertainty_analysis/README.md

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+# Organized uncertainty analysis
+
+This folder is a self-contained, model-first organization of the thesis code. The original files in `FINAL FILES` are preserved unchanged.
+
+Install the reproducible environment with `python -m pip install -r requirements.txt`.
+
+## Structure
+
+```text
+organized_uncertainty_analysis/
+├── data.py
+├── suv_percentilesSLOthenUWM.mat
+├── flags_combined.mat
+├── logistic/
+│   ├── core.py
+│   ├── data_fit_gof.py
+│   ├── ci_estimation.py
+│   ├── elasticity.py
+│   ├── noise_measurement.py
+│   └── notebooks/
+│       ├── 01_data_fit_gof.ipynb
+│       ├── 02_ci_estimation.ipynb
+│       ├── 03_elasticity.ipynb
+│       └── 04_noise_measurement.ipynb
+├── bayesian/
+│   ├── core.py
+│   ├── noise_core.py
+│   ├── data_fit_gof.py
+│   ├── ci_estimation.py
+│   ├── elasticity.py
+│   ├── noise_measurement.py
+│   └── notebooks/
+│       ├── 01_data_fit_gof.ipynb
+│       ├── 02_ci_estimation.ipynb
+│       ├── 03_elasticity.ipynb
+│       └── 04_noise_measurement.ipynb
+└── outputs/
+```
+
+## Recommended order
+
+Run notebooks `01` through `04` within either model folder. Each notebook is self-contained and locates the project root automatically. Expensive replication counts are defined near the top of the relevant notebook so test and thesis runs can be distinguished clearly.
+
+To reproduce all committed tables and figures without Jupyter, run
+`python run_all_notebooks.py` from the project root. Generated PNG/PDF figures
+and CSV tables are written to `outputs/`. Keep these outputs under version
+control when they are part of the thesis results.
+
+## Module responsibilities
+
+- `data_fit_gof.py`: data loading, FULL/TRIM construction, fitting, prediction, and goodness-of-fit.
+- `ci_estimation.py`: Wald, MCA, NPBS, PBS, parameter intervals, risk bands, and intervals for derived characteristics.
+- `elasticity.py`: local elasticity of `x50` and `s50`.
+- `noise_measurement.py`: additive and multiplicative biomarker-noise propagation.
+- `core.py`: preserved underlying implementation used by the four focused public modules.
+
+All generated tables and figures should be written to the top-level `outputs/` directory.

organized_uncertainty_analysis/__init__.py

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+"""Organized uncertainty-analysis package for the thesis."""

organized_uncertainty_analysis/bayesian/__init__.py

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+"""Constrained Bayesian analysis modules."""

organized_uncertainty_analysis/bayesian/ci_estimation.py

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+"""Wald, stabilized MCA, NPBS, PBS, risk-band, x50, and s50 calculations."""
+
+from .core import (
+    hess_fd,
+    jac_fd,
+    grad_scalar_fd,
+    covariance_from_hessian,
+    estimate_ci_bundle,
+    run_bayesian_ci,
+    make_parameter_ci_table,
+    make_derived_ci_table,
+    print_ci_diagnostics,
+    plot_bayesian_ci,
+)

organized_uncertainty_analysis/bayesian/core.py

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+# bayesian.py
+# ============================================================
+# CONDITIONAL BAYESIAN RISK FIT + CONSISTENT CI
+# ============================================================
+
+# bayesian_final_clean.py
+# ============================================================
+# FINAL CONSTRAINED CONDITIONAL RISK MODEL + UNCERTAINTY
+# ============================================================
+#
+# Model fitted by MAP:
+#   Y | X=x ~ Bernoulli(P(AE | X=x))
+#
+# Constraints are enforced through an unconstrained parameter vector phi.
+# The risk function P(AE | X=x) is derived from Bayes' rule.
+#
+# Uncertainty:
+#   - local Wald/delta approximation in phi-space
+#   - nonparametric pairs bootstrap (NPBS)
+#   - generative constrained-Bayesian parametric bootstrap (PBS)
+#
+# Every clean and bootstrap dataset uses the same conditional MAP estimator.
+# Bootstrap refits begin at the clean fit and use seeded fallback starts.
+# ============================================================
+
+import os
+import time
+import warnings
+import numpy as np
+import pandas as pd
+import matplotlib.pyplot as plt
+from matplotlib.lines import Line2D
+
+from scipy import optimize, stats
+from scipy.ndimage import gaussian_filter1d
+from scipy.io import loadmat
+from scipy.optimize import brentq
+from scipy.special import betaln, gammaln
+
+from ..data import get_data
+
+
+# ============================================================
+# 1) DATA
+# ============================================================
+
+def load_xy(
+    perc=95,
+    suv_path="suv_percentilesSLOthenUWM.mat",
+    flags_path="flags_combined.mat",
+):
+    here = os.path.dirname(os.path.dirname(os.path.abspath(__file__)))
+    suv_full = os.path.join(here, suv_path)
+    flags_full = os.path.join(here, flags_path)
+
+    print("Loading SUV from:", suv_full)
+    print("Loading FLAGS from:", flags_full)
+
+    suv_dict = loadmat(suv_full)
+    flags_dict = loadmat(flags_full)
+
+    X, y = get_data(perc, suv_dict, flags_dict)
+    X = np.asarray(X, float).ravel()
+    y = np.asarray(y, int).ravel()
+
+    mask = np.isfinite(X)
+    X, y = X[mask], y[mask]
+    X = np.clip(X, 1e-12, None)
+
+    return X, y
+
+
+def make_trimmed_dataset(X, y, value_to_drop=2.48122597, tol=1e-3):
+    X = np.asarray(X, float)
+    y = np.asarray(y, int)
+
+    mask_keep = np.abs(X - value_to_drop) > tol
+
+    return {
+        "X_orig": X.copy(),
+        "y_orig": y.copy(),
+        "X_trim": X[mask_keep],
+        "y_trim": y[mask_keep],
+        "removed_idx": np.where(~mask_keep)[0],
+    }
+
+
+# ============================================================
+# 2) PARAMETERIZATION AND MODEL
+# ============================================================
+
+def sigmoid(t):
+    return 1.0 / (1.0 + np.exp(-np.clip(t, -60.0, 60.0)))
+
+
+def softplus(t):
+    t = np.asarray(t, float)
+    return np.log1p(np.exp(-np.abs(t))) + np.maximum(t, 0.0)
+
+
+def theta_max(a, b, k, s, eps=1e-12):
+    """Monotonicity cap for vartheta."""
+    A = a - k
+    if A <= 0.0:
+        return np.inf
+
+    r = np.sqrt(a + b) - np.sqrt(max(A, eps))
+    return np.inf if r <= 1e-12 else s / (r * r)
+
+
+def unpack(phi):
+    """
+    Map unconstrained phi to scientific parameters.
+
+    phi = [omega_raw, b_raw, s_raw, k_raw, delta_raw, r_raw]
+
+    omega in (0,1)
+    b,s,k > 0
+    a = k + delta, delta > 0
+    vartheta = vartheta_cap * sigmoid(r_raw)
+    """
+    omega_raw, b_raw, s_raw, k_raw, delta_raw, r_raw = np.asarray(phi, float)
+
+    omega = sigmoid(omega_raw)
+
+    b = float(softplus(b_raw) + 1e-6)
+    s = float(softplus(s_raw) + 1e-6)
+    k = float(softplus(k_raw) + 1e-6)
+
+    delta = float(softplus(delta_raw) + 1e-6)
+    a = k + delta
+
+    vartheta_cap = theta_max(a, b, k, s)
+    vartheta = vartheta_cap * sigmoid(r_raw)
+
+    return omega, a, b, s, k, vartheta, vartheta_cap
+
+
+def dE_full(x, a, b, s, k, vartheta):
+    """log f_AE(x) - log f_NC(x), including normalizing constants."""
+    x = np.asarray(x, float)
+
+    return (
+        (a - k) * np.log(x)
+        - (a + b) * np.log1p(x / s)
+        + x / vartheta
+        - a * np.log(s)
+        - betaln(a, b)
+        + k * np.log(vartheta)
+        + gammaln(k)
+    )
+
+
+def P_with(theta_hat, x):
+    """Derived risk function P(AE | X=x)."""
+    omega, a, b, s, k, vartheta, _ = theta_hat
+    x = np.asarray(x, float)
+
+    logit_omega = np.log(omega) - np.log1p(-omega)
+    eta = logit_omega + dE_full(x, a, b, s, k, vartheta)
+
+    return sigmoid(eta)
+
+
+def make_priors(y, tau=25.0):
+    """Beta(tau*p_emp, tau*(1-p_emp)) prior on prevalence omega."""
+    p_emp = float(np.mean(y))
+    alpha = max(tau * p_emp, 1e-6)
+    beta = max(tau * (1.0 - p_emp), 1e-6)
+    return alpha, beta
+
+
+def init_phi(X, y):
+    """Stable generic start in unconstrained coordinates."""
+    X = np.asarray(X, float)
+    y = np.asarray(y, int)
+
+    X0 = X[y == 0]
+    m0 = X0.mean() if X0.size else X.mean()
+    v0 = X0.var() if X0.size else X.var()
+    k0 = 2.0 if v0 <= 0 else max((m0 * m0) / (v0 + 1e-9), 1.5)
+
+    X1 = X[y == 1]
+    m1 = np.median(X1) if X1.size else np.median(X)
+
+    omega0 = np.clip(float(np.mean(y)), 1e-3, 1.0 - 1e-3)
+    b0 = 1.5
+    s0 = max(m1, 0.5)
+
+    return np.array(
+        [
+            np.log(omega0 / (1.0 - omega0)),
+            np.log(np.expm1(b0) + 1e-9),
+            np.log(np.expm1(s0) + 1e-9),
+            np.log(np.expm1(k0) + 1e-9),
+            np.log(np.expm1(1.0) + 1e-9),
+            -0.2,
+        ],
+        dtype=float,
+    )
+
+
+# ============================================================
+# 3) CONDITIONAL NEGATIVE LOG-POSTERIOR
+# ============================================================
+
+def neg_post(
+    phi,
+    X,
+    y,
+    alpha,
+    beta,
+    use_prior_p=True,
+    prior_r=(1.05, 1.05),
+):
+    """Conditional Bernoulli negative log-posterior for P(Y=1 | X)."""
+    phi = np.asarray(phi, float).reshape(-1)
+    X = np.asarray(X, float).reshape(-1)
+    y = np.asarray(y, int).reshape(-1)
+
+    if (
+        phi.size != 6
+        or X.size != y.size
+        or not np.all(np.isfinite(phi))
+        or not np.all(np.isfinite(X))
+        or np.any(X <= 0.0)
+    ):
+        return 1e100
+
+    try:
+        omega, a, b, s, k, vartheta, vartheta_cap = unpack(phi)
+    except Exception:
+        return 1e100
+
+    pars = np.asarray(
+        [omega, a, b, s, k, vartheta, vartheta_cap],
+        float,
+    )
+
+    if not np.all(np.isfinite(pars)):
+        return 1e100
+
+    if not (
+        0.0 < omega < 1.0
+        and a > k > 0.0
+        and b > 0.0
+        and s > 0.0
+        and vartheta > 0.0
+        and vartheta_cap > 0.0
+        and vartheta < vartheta_cap
+    ):
+        return 1e100
+
+    eps = 1e-12
+    omega_safe = float(np.clip(omega, eps, 1.0 - eps))
+    eta = (
+        np.log(omega_safe)
+        - np.log1p(-omega_safe)
+        + dE_full(X, a, b, s, k, vartheta)
+    )
+    probability = np.clip(sigmoid(eta), eps, 1.0 - eps)
+    loglik = float(
+        np.sum(y * np.log(probability) + (1 - y) * np.log1p(-probability))
+    )
+
+    logprior = 0.0
+
+    if use_prior_p:
+        logprior += float(
+            (alpha - 1.0) * np.log(omega_safe)
+            + (beta - 1.0) * np.log1p(-omega_safe)
+        )
+
+    if prior_r is not None:
+        r = vartheta / vartheta_cap
+
+        if not np.isfinite(r) or not (0.0 < r < 1.0):
+            return 1e100
+
+        r = float(np.clip(r, 1e-12, 1.0 - 1e-12))
+
+        logprior += float(
+            (prior_r[0] - 1.0) * np.log(r)
+            + (prior_r[1] - 1.0) * np.log1p(-r)
+        )
+
+    value = -(loglik + logprior)
+    return float(value) if np.isfinite(value) else 1e100
+
+
+# ============================================================
+# 4) MAP FITTING
+# ============================================================
+
+def fit_bayes(
+    X,
+    y,
+    seed=0,
+    use_prior_p=True,
+    prior_r=(1.05, 1.05),
+    tau=25.0,
+    phi_start=None,
+    n_starts=1,
+    maxiter=6000,
+    ftol=1e-9,
+    gtol=1e-8,
+    maxls=50,
+    refine=False,
+    prior_alpha_beta=None,
+):
+    """Fit the conditional MAP estimator with deterministic multi-starts.
+
+    ``phi_start`` is used first when supplied (notably for bootstrap refits).
+    Additional starts are seeded perturbations, and the best converged fit is
+    returned. This keeps the estimator consistent across all datasets while
+    making the previously exposed fitting arguments effective.
+    """
+    X = np.asarray(X, float).reshape(-1)
+    y = np.asarray(y, int).reshape(-1)
+
+    valid = np.isfinite(X) & (X > 0.0)
+    X, y = X[valid], y[valid]
+
+    if X.size == 0 or X.size != y.size:
+        raise ValueError("Invalid or empty dataset.")
+    if np.unique(y).size < 2:
+        raise ValueError("Both outcome classes are required.")
+
+    if prior_alpha_beta is None:
+        alpha, beta = make_priors(y, tau=tau)
+    else:
+        alpha, beta = map(float, prior_alpha_beta)
+
+    objective = lambda w: neg_post(
+        w,
+        X,
+        y,
+        alpha,
+        beta,
+        use_prior_p=use_prior_p,
+        prior_r=prior_r,
+    )
+
+    del refine
+    rng = np.random.default_rng(seed)
+    default_start = init_phi(X, y)
+    first_start = (
+        np.asarray(phi_start, float).reshape(-1)
+        if phi_start is not None else default_start
+    )
+    if first_start.size != 6 or not np.all(np.isfinite(first_start)):
+        raise ValueError("phi_start must contain six finite values.")
+
+    starts = [first_start]
+    if phi_start is not None and int(n_starts) > 1:
+        starts.append(default_start)
+    while len(starts) < max(1, int(n_starts)):
+        starts.append(first_start + rng.normal(0.0, 0.2, size=6))
+
+    results = []
+    options = {
+        "maxiter": int(maxiter),
+        "ftol": float(ftol),
+        "gtol": float(gtol),
+        "maxls": int(maxls),
+    }
+    for start in starts:
+        candidate = optimize.minimize(
+            objective, start, method="L-BFGS-B", options=options
+        )
+        if candidate.success and np.isfinite(candidate.fun):
+            results.append(candidate)
+
+    if not results:
+        fallback = first_start + rng.normal(0.0, 0.2, size=6)
+        candidate = optimize.minimize(
+            objective, fallback, method="L-BFGS-B", options=options
+        )
+        if candidate.success and np.isfinite(candidate.fun):
+            results.append(candidate)
+
+    if not results:
+        raise RuntimeError("Conditional MAP fit did not converge.")
+
+    res = min(results, key=lambda item: float(item.fun))
+    return unpack(res.x), res
+
+
+def _fit_bootstrap(
+    Xb,
+    yb,
+    phi_clean,
+    seed,
+    use_prior_p,
+    prior_r,
+    tau,
+    n_starts_boot=5,
+    prior_alpha_beta=None,
+):
+    """Refit a bootstrap dataset using the clean fit as the first start."""
+    return fit_bayes(
+        Xb,
+        yb,
+        seed=seed,
+        use_prior_p=use_prior_p,
+        prior_r=prior_r,
+        tau=tau,
+        phi_start=phi_clean,
+        n_starts=n_starts_boot,
+        maxiter=6000,
+        ftol=1e-9,
+        gtol=1e-7,
+        maxls=50,
+        refine=False,
+        prior_alpha_beta=prior_alpha_beta,
+    )
+
+
+# ============================================================
+# 5) DERIVED QUANTITIES
+# ============================================================
+
+def x_at_p(
+    theta_hat,
+    p_target=0.5,
+    lo=1e-8,
+    hi=6.0,
+    hi_max=100.0,
+    expansion_factor=2.0,
+):
+    lo = max(float(lo), 1e-12)
+    hi = max(float(hi), lo * 1.01)
+    hi_max = max(float(hi_max), hi)
+
+    def f(x):
+        return float(np.asarray(P_with(theta_hat, x))) - float(p_target)
+
+    try:
+        f_lo = f(lo)
+        f_hi = f(hi)
+
+        if not (np.isfinite(f_lo) and np.isfinite(f_hi)):
+            return np.nan
+
+        while f_lo > 0.0 and lo > 1e-12:
+            lo_new = max(lo / expansion_factor, 1e-12)
+            if lo_new == lo:
+                break
+            lo = lo_new
+            f_lo = f(lo)
+
+        while f_hi < 0.0 and hi < hi_max:
+            hi_new = min(hi * expansion_factor, hi_max)
+            if hi_new == hi:
+                break
+            hi = hi_new
+            f_hi = f(hi)
+
+        if f_lo == 0.0:
+            return lo
+        if f_hi == 0.0:
+            return hi
+        if f_lo * f_hi > 0.0:
+            return np.nan
+
+        return float(brentq(f, lo, hi))
+
+    except Exception:
+        return np.nan
+
+
+def slope_at_x(theta_hat, x0):
+    if not np.isfinite(x0) or x0 <= 0.0:
+        return np.nan
+
+    h = 1e-4 * max(1.0, abs(float(x0)))
+    xm = max(float(x0) - h, 1e-12)
+    xp = float(x0) + h
+
+    try:
+        pm = float(P_with(theta_hat, xm))
+        pp = float(P_with(theta_hat, xp))
+        return float((pp - pm) / (xp - xm))
+    except Exception:
+        return np.nan
+
+
+# ============================================================
+# 6) NUMERICAL DIFFERENTIATION / WALD
+# ============================================================
+
+def hess_fd(F, x):
+    x = np.asarray(x, float).reshape(-1)
+    n = x.size
+    H = np.zeros((n, n), float)
+    h = 1e-4 * (1.0 + np.abs(x))
+
+    def grad(G, z):
+        g = np.full(n, np.nan)
+        for j in range(n):
+            zp, zm = z.copy(), z.copy()
+            zp[j] += h[j]
+            zm[j] -= h[j]
+            fp, fm = G(zp), G(zm)
+            if np.isfinite(fp) and np.isfinite(fm):
+                g[j] = (fp - fm) / (2.0 * h[j])
+        return g
+
+    for i in range(n):
+        xp, xm = x.copy(), x.copy()
+        xp[i] += h[i]
+        xm[i] -= h[i]
+        H[:, i] = (grad(F, xp) - grad(F, xm)) / (2.0 * h[i])
+
+    return 0.5 * (H + H.T)
+
+
+def jac_fd(Fvec, w):
+    w = np.asarray(w, float).reshape(-1)
+    f0 = np.asarray(Fvec(w), float).reshape(-1)
+    J = np.zeros((f0.size, w.size), float)
+    h = 1e-4 * (1.0 + np.abs(w))
+
+    for j in range(w.size):
+        wp, wm = w.copy(), w.copy()
+        wp[j] += h[j]
+        wm[j] -= h[j]
+
+        fp = np.asarray(Fvec(wp), float).reshape(-1)
+        fm = np.asarray(Fvec(wm), float).reshape(-1)
+
+        J[:, j] = (fp - fm) / (2.0 * h[j])
+
+    return J
+
+
+def grad_scalar_fd(F, w):
+    w = np.asarray(w, float).reshape(-1)
+    g = np.full(w.size, np.nan)
+    h = 1e-4 * (1.0 + np.abs(w))
+
+    for j in range(w.size):
+        wp, wm = w.copy(), w.copy()
+        wp[j] += h[j]
+        wm[j] -= h[j]
+        fp, fm = F(wp), F(wm)
+
+        if np.isfinite(fp) and np.isfinite(fm):
+            g[j] = (fp - fm) / (2.0 * h[j])
+
+    return g
+
+
+def covariance_from_hessian(
+    H,
+    max_condition=1e6,
+    condition_warn=1e8,
+):
+    """Positive spectral stabilization followed by covariance inversion.
+
+    Eigenvalues smaller than ``lambda_max / max_condition`` (including
+    negative eigenvalues) are replaced by that positive floor. The selected
+    condition limit is recorded so regularized Wald/MCA results remain fully
+    auditable and can be subjected to a sensitivity analysis.
+    """
+    H = np.asarray(H, float)
+    H = 0.5 * (H + H.T)
+
+    eigvals, eigvecs = np.linalg.eigh(H)
+
+    if not np.all(np.isfinite(eigvals)):
+        raise RuntimeError("Non-finite Hessian eigenvalues.")
+
+    max_abs = float(np.max(np.abs(eigvals)))
+    if not np.isfinite(max_abs) or max_abs <= 0.0:
+        raise RuntimeError("Hessian has no usable curvature.")
+
+    positive = eigvals[eigvals > 0.0]
+    original_condition = (
+        float(eigvals.max() / positive.min())
+        if positive.size == eigvals.size else np.inf
+    )
+    max_condition = float(max_condition)
+    if not np.isfinite(max_condition) or max_condition <= 1.0:
+        raise ValueError("max_condition must be a finite number greater than 1.")
+    eig_floor = max(max_abs / max_condition, 1e-12)
+    eigvals_stable = np.maximum(eigvals, eig_floor)
+    stabilized = bool(np.any(eigvals < eig_floor))
+    condition = float(eigvals_stable.max() / eigvals_stable.min())
+
+    reliable = bool(
+        np.all(eigvals > 0.0)
+        and np.isfinite(original_condition)
+        and original_condition <= max_condition
+        and not stabilized
+    )
+    if not reliable:
+        warnings.warn(
+            f"Hessian is weak or indefinite and required spectral "
+            f"stabilization (original condition={original_condition:.3e}; "
+            f"stabilized condition={condition:.3e}). "
+            "Interpret Wald/MCA as local sensitivity approximations.",
+            RuntimeWarning,
+        )
+
+    Sigma = eigvecs @ np.diag(1.0 / eigvals_stable) @ eigvecs.T
+    Sigma = 0.5 * (Sigma + Sigma.T)
+
+    diagnostics = {
+        "eigenvalues": eigvals,
+        "minimum_eigenvalue": float(eigvals.min()),
+        "maximum_eigenvalue": float(eigvals.max()),
+        "condition_number": condition,
+        "original_condition_number": original_condition,
+        "positive_definite": bool(np.all(eigvals > 0.0)),
+        "original_positive_definite": bool(np.all(eigvals > 0.0)),
+        "stabilized": stabilized,
+        "eigenvalue_floor": eig_floor,
+        "stabilized_eigenvalues": eigvals_stable,
+        "reliable": reliable,
+        "maximum_allowed_condition": max_condition,
+    }
+
+    return Sigma, diagnostics
+
+
+def reported_theta_from_phi(phi):
+    omega, a, b, s, k, vartheta, _ = unpack(phi)
+    return np.array([omega, a, b, s, k, vartheta], float)
+
+
+def reported_theta_from_hat(theta_hat):
+    omega, a, b, s, k, vartheta, _ = theta_hat
+    return np.array([omega, a, b, s, k, vartheta], float)
+
+
+def _wald_scalar(estimate, gradient, covariance, z):
+    gradient = np.asarray(gradient, float)
+
+    if not np.isfinite(estimate) or not np.all(np.isfinite(gradient)):
+        return np.nan, np.nan
+
+    var = float(gradient @ covariance @ gradient)
+
+    if not np.isfinite(var) or var < -1e-12:
+        return np.nan, np.nan
+
+    se = np.sqrt(max(var, 0.0))
+    return float(estimate - z * se), float(estimate + z * se)
+
+
+# ============================================================
+# 7) CI FOR ONE DATASET
+# ============================================================
+
+def estimate_ci_bundle(
+    X,
+    y,
+    label,
+    x_grid,
+    B_nonpar=400,
+    B_param=400,
+    M_mca=10000,
+    mca_seed=None,
+    seed=123,
+    use_prior_p=True,
+    prior_r=(1.05, 1.05),
+    tau=25.0,
+    alpha_ci=0.05,
+    n_starts_clean=1,
+    n_starts_boot=1,
+    progress_every=25,
+    max_attempt_multiplier=20,
+    max_hessian_condition=1e6,
+):
+    X = np.asarray(X, float).reshape(-1)
+    y = np.asarray(y, int).reshape(-1)
+    x_grid = np.asarray(x_grid, float).reshape(-1)
+
+    rng = np.random.default_rng(seed)
+    n = X.size
+
+    z = float(stats.norm.ppf(1.0 - alpha_ci / 2.0))
+    qlo, qhi = 100.0 * alpha_ci / 2.0, 100.0 * (1.0 - alpha_ci / 2.0)
+
+    # ---------------- CLEAN MAP ----------------
+    t0 = time.time()
+    theta_hat, res = fit_bayes(
+        X,
+        y,
+        seed=seed,
+        use_prior_p=use_prior_p,
+        prior_r=prior_r,
+        tau=tau,
+        n_starts=n_starts_clean,
+        refine=False,
+    )
+
+    phi_hat = np.asarray(res.x, float)
+    theta_hat_vec = reported_theta_from_phi(phi_hat)
+
+    pmap = np.asarray(P_with(theta_hat, x_grid), float)
+    # Freeze the empirical-Bayes prior calibrated on the original dataset.
+    # Bootstrap samples vary through resampling/simulation, not by redefining
+    # the prior from each replicate's random event count.
+    prior_alpha_beta = make_priors(y, tau=tau)
+    x50_hat = x_at_p(theta_hat, 0.5, hi=max(6.0, float(x_grid.max())))
+    s50_hat = slope_at_x(theta_hat, x50_hat)
+
+    print(f"{label}: clean MAP completed in {(time.time()-t0):.1f} s")
+
+    # ---------------- WALD ----------------
+    alpha_p, beta_p = make_priors(y, tau=tau)
+
+    objective = lambda w: neg_post(
+        w, X, y, alpha_p, beta_p,
+        use_prior_p=use_prior_p,
+        prior_r=prior_r,
+    )
+
+    H = hess_fd(objective, phi_hat)
+
+    wald_available = True
+    try:
+        Sigma_phi, hdiag = covariance_from_hessian(
+            H, max_condition=max_hessian_condition
+        )
+
+        J_curve = jac_fd(lambda w: P_with(unpack(w), x_grid), phi_hat)
+        var_curve = np.einsum("ij,jk,ik->i", J_curve, Sigma_phi, J_curve)
+        se_curve = np.sqrt(np.maximum(var_curve, 0.0))
+        wald_lo = np.clip(pmap - z * se_curve, 0.0, 1.0)
+        wald_hi = np.clip(pmap + z * se_curve, 0.0, 1.0)
+
+        J_theta = jac_fd(reported_theta_from_phi, phi_hat)
+        Sigma_theta = J_theta @ Sigma_phi @ J_theta.T
+        Sigma_theta = 0.5 * (Sigma_theta + Sigma_theta.T)
+
+        se_theta = np.sqrt(np.maximum(np.diag(Sigma_theta), 0.0))
+        wald_param_lo = theta_hat_vec - z * se_theta
+        wald_param_hi = theta_hat_vec + z * se_theta
+
+        def x50_phi(w):
+            return x_at_p(
+                unpack(w),
+                0.5,
+                hi=max(6.0, float(x_grid.max())),
+            )
+
+        gx = grad_scalar_fd(x50_phi, phi_hat)
+        wald_x50_lo, wald_x50_hi = _wald_scalar(
+            x50_hat, gx, Sigma_phi, z
+        )
+
+        def s50_phi(w):
+            th = unpack(w)
+            xx = x_at_p(
+                th,
+                0.5,
+                hi=max(6.0, float(x_grid.max())),
+            )
+            return slope_at_x(th, xx)
+
+        gs = grad_scalar_fd(s50_phi, phi_hat)
+        wald_s50_lo, wald_s50_hi = _wald_scalar(
+            s50_hat, gs, Sigma_phi, z
+        )
+
+    except RuntimeError as exc:
+        warnings.warn(f"{label}: Wald unavailable: {exc}", RuntimeWarning)
+        wald_available = False
+        Sigma_phi = np.full((6, 6), np.nan)
+        Sigma_theta = np.full((6, 6), np.nan)
+        hdiag = {}
+        wald_lo = wald_hi = np.full_like(pmap, np.nan)
+        wald_param_lo = wald_param_hi = np.full(6, np.nan)
+        wald_x50_lo = wald_x50_hi = np.nan
+        wald_s50_lo = wald_s50_hi = np.nan
+
+    # ---------------- MONTE CARLO APPROXIMATION ----------------
+    # Laplace/normal propagation using the same covariance as Wald. The
+    # diagnostics state explicitly when historical spectral stabilization was
+    # required before inversion.
+    mca_curves, mca_theta, mca_x50, mca_s50 = [], [], [], []
+    mca_attempted = int(M_mca)
+    if mca_seed is None:
+        mca_seed = int(seed) + 10_000
+
+    if wald_available and int(M_mca) > 0:
+        rng_mca = np.random.default_rng(mca_seed)
+        try:
+            phi_draws = rng_mca.multivariate_normal(
+                mean=phi_hat,
+                cov=Sigma_phi,
+                size=int(M_mca),
+                check_valid="raise",
+            )
+            for draw in np.atleast_2d(phi_draws):
+                try:
+                    thm = unpack(draw)
+                    curve = np.asarray(P_with(thm, x_grid), float)
+                    xx = x_at_p(
+                        thm, 0.5, hi=max(6.0, float(x_grid.max()))
+                    )
+                    ss = slope_at_x(thm, xx)
+                    theta_vec = reported_theta_from_hat(thm)
+                    if (
+                        np.all(np.isfinite(curve))
+                        and np.all(np.isfinite(theta_vec))
+                        and np.isfinite(xx)
+                        and np.isfinite(ss)
+                    ):
+                        mca_curves.append(curve)
+                        mca_theta.append(theta_vec)
+                        mca_x50.append(xx)
+                        mca_s50.append(ss)
+                except Exception:
+                    continue
+        except Exception as exc:
+            warnings.warn(f"{label}: MCA unavailable: {exc}", RuntimeWarning)
+
+    mca_curves = np.asarray(mca_curves, float)
+    mca_theta = np.asarray(mca_theta, float)
+    mca_x50 = np.asarray(mca_x50, float)
+    mca_s50 = np.asarray(mca_s50, float)
+    mca_lo = (
+        np.percentile(mca_curves, qlo, axis=0) if len(mca_curves) else None
+    )
+    mca_hi = (
+        np.percentile(mca_curves, qhi, axis=0) if len(mca_curves) else None
+    )
+    diagnostics_mca = {
+        "scheme": "local_Gaussian_phi_with_spectral_stabilization",
+        "target": int(M_mca),
+        "attempted": mca_attempted,
+        "successful_curve": len(mca_curves),
+        "successful_x50": len(mca_x50),
+        "successful_s50": len(mca_s50),
+        "available": bool(len(mca_curves) > 0),
+        "reason_if_unavailable": (
+            None if len(mca_curves) else
+            "No usable covariance or no finite Monte Carlo draws"
+        ),
+    }
+
+    # ---------------- NPBS ----------------
+    np_curves, np_theta, np_x50, np_s50 = [], [], [], []
+    attempted_np = rejected_single_np = rejected_fit_np = 0
+    t_np = time.time()
+
+    max_attempts_np = max(int(B_nonpar), int(max_attempt_multiplier * B_nonpar))
+    while len(np_curves) < int(B_nonpar) and attempted_np < max_attempts_np:
+        attempted_np += 1
+
+        idx = rng.integers(0, n, size=n)
+        Xb, yb = X[idx], y[idx]
+
+        if np.unique(yb).size < 2:
+            rejected_single_np += 1
+            continue
+
+        try:
+            thb, rb = _fit_bootstrap(
+                Xb, yb, phi_hat,
+                int(rng.integers(0, 10_000_000)),
+                use_prior_p, prior_r, tau,
+                n_starts_boot=n_starts_boot,
+                prior_alpha_beta=prior_alpha_beta,
+            )
+
+            curve = np.asarray(P_with(thb, x_grid), float)
+            xx = x_at_p(thb, 0.5, hi=max(6.0, float(x_grid.max())))
+            ss = slope_at_x(thb, xx)
+
+            if not (
+                np.all(np.isfinite(curve))
+                and np.isfinite(xx)
+                and np.isfinite(ss)
+            ):
+                rejected_fit_np += 1
+                continue
+
+            np_curves.append(curve)
+            np_theta.append(reported_theta_from_hat(thb))
+            np_x50.append(xx)
+            np_s50.append(ss)
+
+            if progress_every and len(np_curves) % progress_every == 0:
+                elapsed = (time.time() - t_np) / 60.0
+                print(
+                    f"{label} NPBS: {len(np_curves)}/{B_nonpar} "
+                    f"({elapsed:.1f} min)"
+                )
+
+        except Exception:
+            rejected_fit_np += 1
+
+    # ---------------- PBS ----------------
+    pb_curves, pb_theta, pb_x50, pb_s50 = [], [], [], []
+    attempted_pb = rejected_single_pb = rejected_fit_pb = 0
+    omega_hat, a_hat, b_hat, s_hat, k_hat, vartheta_hat, _ = theta_hat
+    t_pb = time.time()
+
+    max_attempts_pb = max(int(B_param), int(max_attempt_multiplier * B_param))
+    while len(pb_curves) < int(B_param) and attempted_pb < max_attempts_pb:
+        attempted_pb += 1
+
+        # Generative CB-PBS from the fitted prevalence and class-conditional
+        # biomarker distributions, as specified in the methodology.
+        yb = rng.binomial(1, omega_hat, size=n).astype(int)
+
+        if np.unique(yb).size < 2:
+            rejected_single_pb += 1
+            continue
+
+        Xb = np.empty(n, float)
+        is_nc = yb == 0
+        is_ae = ~is_nc
+        Xb[is_nc] = rng.gamma(
+            shape=k_hat, scale=vartheta_hat, size=int(is_nc.sum())
+        )
+        numerator = rng.gamma(shape=a_hat, scale=1.0, size=int(is_ae.sum()))
+        denominator = rng.gamma(shape=b_hat, scale=1.0, size=int(is_ae.sum()))
+        Xb[is_ae] = s_hat * numerator / denominator
+
+        try:
+            thb, rb = _fit_bootstrap(
+                Xb, yb, phi_hat,
+                int(rng.integers(0, 10_000_000)),
+                use_prior_p, prior_r, tau,
+                n_starts_boot=n_starts_boot,
+                prior_alpha_beta=prior_alpha_beta,
+            )
+
+            curve = np.asarray(P_with(thb, x_grid), float)
+            xx = x_at_p(thb, 0.5, hi=max(6.0, float(x_grid.max())))
+            ss = slope_at_x(thb, xx)
+
+            if not (
+                np.all(np.isfinite(curve))
+                and np.isfinite(xx)
+                and np.isfinite(ss)
+            ):
+                rejected_fit_pb += 1
+                continue
+
+            pb_curves.append(curve)
+            pb_theta.append(reported_theta_from_hat(thb))
+            pb_x50.append(xx)
+            pb_s50.append(ss)
+
+            if progress_every and len(pb_curves) % progress_every == 0:
+                elapsed = (time.time() - t_pb) / 60.0
+                print(
+                    f"{label} PBS: {len(pb_curves)}/{B_param} "
+                    f"({elapsed:.1f} min)"
+                )
+
+        except Exception:
+            rejected_fit_pb += 1
+
+    np_curves = np.asarray(np_curves, float)
+    np_theta = np.asarray(np_theta, float)
+    np_x50 = np.asarray(np_x50, float)
+    np_s50 = np.asarray(np_s50, float)
+
+    pb_curves = np.asarray(pb_curves, float)
+    pb_theta = np.asarray(pb_theta, float)
+    pb_x50 = np.asarray(pb_x50, float)
+    pb_s50 = np.asarray(pb_s50, float)
+
+    np_lo = np.percentile(np_curves, qlo, axis=0) if len(np_curves) else None
+    np_hi = np.percentile(np_curves, qhi, axis=0) if len(np_curves) else None
+
+    pb_lo = np.percentile(pb_curves, qlo, axis=0) if len(pb_curves) else None
+    pb_hi = np.percentile(pb_curves, qhi, axis=0) if len(pb_curves) else None
+
+    diagnostics_np = {
+        "scheme": "ordinary_pairs",
+        "target": B_nonpar,
+        "attempted": attempted_np,
+        "successful_curve": len(np_curves),
+        "successful_x50": len(np_x50),
+        "successful_s50": len(np_s50),
+        "rejected_single_class": rejected_single_np,
+        "rejected_fit": rejected_fit_np,
+        "completed_target": bool(len(np_curves) == int(B_nonpar)),
+        "max_attempts": max_attempts_np,
+    }
+
+    diagnostics_pb = {
+        "scheme": "generative_CB_prevalence_and_class_conditional_X",
+        "target": B_param,
+        "attempted": attempted_pb,
+        "successful_curve": len(pb_curves),
+        "successful_x50": len(pb_x50),
+        "successful_s50": len(pb_s50),
+        "rejected_single_class": rejected_single_pb,
+        "rejected_fit": rejected_fit_pb,
+        "completed_target": bool(len(pb_curves) == int(B_param)),
+        "max_attempts": max_attempts_pb,
+    }
+
+    return {
+        "label": label,
+        "theta_hat": theta_hat,
+        "theta_hat_vec": theta_hat_vec,
+        "phi_hat": phi_hat,
+        "res": res,
+        "objective": float(res.fun),
+
+        "x50": x50_hat,
+        "s50": s50_hat,
+        "pmap": pmap,
+
+        "wald_available": wald_available,
+        "wald_lo": wald_lo,
+        "wald_hi": wald_hi,
+        "wald_param_lo": wald_param_lo,
+        "wald_param_hi": wald_param_hi,
+        "wald_x50_lo": wald_x50_lo,
+        "wald_x50_hi": wald_x50_hi,
+        "wald_s50_lo": wald_s50_lo,
+        "wald_s50_hi": wald_s50_hi,
+
+        "np_lo": np_lo,
+        "np_hi": np_hi,
+        "pb_lo": pb_lo,
+        "pb_hi": pb_hi,
+        "mca_lo": mca_lo,
+        "mca_hi": mca_hi,
+
+        "theta_np": np_theta,
+        "theta_pb": pb_theta,
+        "x50_np": np_x50,
+        "x50_pb": pb_x50,
+        "s50_np": np_s50,
+        "s50_pb": pb_s50,
+        "theta_mca": mca_theta,
+        "x50_mca": mca_x50,
+        "s50_mca": mca_s50,
+
+        "used_np": len(np_curves),
+        "used_pb": len(pb_curves),
+        "used_mca": len(mca_curves),
+
+        "diagnostics_np": diagnostics_np,
+        "diagnostics_pb": diagnostics_pb,
+        "diagnostics_mca": diagnostics_mca,
+        "hessian_diagnostics": hdiag,
+        "prior_alpha_beta": prior_alpha_beta,
+        "alpha_ci": float(alpha_ci),
+        "max_hessian_condition": float(max_hessian_condition),
+
+        "H_phi": H,
+        "Sigma_phi": Sigma_phi,
+        "Sigma_theta": Sigma_theta,
+    }
+
+
+# ============================================================
+# 8) FULL + TRIM CI
+# ============================================================
+
+def run_bayesian_ci(
+    perc=95,
+    suv_path="suv_percentilesSLOthenUWM.mat",
+    flags_path="flags_combined.mat",
+    value_to_drop=2.48122597,
+    tol=1e-3,
+    xmax=4.5,
+    n_grid=600,
+    B_nonpar=400,
+    B_param=400,
+    M_mca=10000,
+    mca_seed=None,
+    seed=123,
+    use_prior_p=True,
+    prior_r=(1.05, 1.05),
+    tau=25.0,
+    alpha_ci=0.05,
+    grid_lower_fraction=0.75,
+    n_starts_clean=1,
+    n_starts_boot=1,
+    progress_every=25,
+    max_attempt_multiplier=20,
+    max_hessian_condition=1e6,
+):
+    X_all, y_all = load_xy(
+        perc=perc,
+        suv_path=suv_path,
+        flags_path=flags_path,
+    )
+
+    ds = make_trimmed_dataset(
+        X_all,
+        y_all,
+        value_to_drop=value_to_drop,
+        tol=tol,
+    )
+
+    x_min = max(
+        1e-8,
+        grid_lower_fraction
+        * float(min(ds["X_orig"].min(), ds["X_trim"].min())),
+    )
+
+    x_max = max(
+        float(xmax),
+        float(ds["X_orig"].max()),
+        float(ds["X_trim"].max()),
+    )
+
+    x_grid = np.linspace(x_min, x_max, int(n_grid))
+
+    full = estimate_ci_bundle(
+        ds["X_orig"],
+        ds["y_orig"],
+        "FULL",
+        x_grid,
+        B_nonpar=B_nonpar,
+        B_param=B_param,
+        M_mca=M_mca,
+        mca_seed=(int(seed) + 10_000 if mca_seed is None else int(mca_seed)),
+        seed=seed,
+        use_prior_p=use_prior_p,
+        prior_r=prior_r,
+        tau=tau,
+        alpha_ci=alpha_ci,
+        n_starts_clean=n_starts_clean,
+        n_starts_boot=n_starts_boot,
+        progress_every=progress_every,
+        max_attempt_multiplier=max_attempt_multiplier,
+        max_hessian_condition=max_hessian_condition,
+    )
+
+    trim = estimate_ci_bundle(
+        ds["X_trim"],
+        ds["y_trim"],
+        "TRIM",
+        x_grid,
+        B_nonpar=B_nonpar,
+        B_param=B_param,
+        M_mca=M_mca,
+        mca_seed=(int(seed) + 10_001 if mca_seed is None else int(mca_seed) + 1),
+        seed=seed + 1,
+        use_prior_p=use_prior_p,
+        prior_r=prior_r,
+        tau=tau,
+        alpha_ci=alpha_ci,
+        n_starts_clean=n_starts_clean,
+        n_starts_boot=n_starts_boot,
+        progress_every=progress_every,
+        max_attempt_multiplier=max_attempt_multiplier,
+        max_hessian_condition=max_hessian_condition,
+    )
+
+    return {
+        **ds,
+        "x_grid": x_grid,
+        "orig": full,
+        "trim": trim,
+    }
+
+
+# ============================================================
+# 9) TABLES / DIAGNOSTICS
+# ============================================================
+
+PARAMETER_NAMES = ["omega", "a", "b", "s", "k", "vartheta"]
+
+
+HISTORICAL_REFERENCE = {
+    "FULL": {
+        "objective": 9.612766,
+        "theta": np.array([
+            0.05013031639340312,
+            835.7394119971459,
+            812.0599466844761,
+            1.5849829783592195,
+            260.69110931079496,
+            0.005737139709007281,
+        ]),
+        "x50": 1.7923,
+    },
+    "TRIM": {
+        "objective": 7.423491,
+        "theta": np.array([
+            0.050915239967693926,
+            547.8229343628883,
+            297.1652388267381,
+            0.9319626391393511,
+            116.9852193858385,
+            0.012177886089862443,
+        ]),
+        "x50": 1.7541,
+    },
+}
+
+
+def check_historical_reference(ci_res, rtol=5e-3, atol=5e-4):
+    """Compare the clean fit with the saved approved notebook results."""
+    rows = []
+    for key, dataset in (("orig", "FULL"), ("trim", "TRIM")):
+        out = ci_res[key]
+        ref = HISTORICAL_REFERENCE[dataset]
+        theta = np.asarray(out["theta_hat_vec"], float)
+        rows.append({
+            "Dataset": dataset,
+            "Objective": float(out["objective"]),
+            "Reference_objective": ref["objective"],
+            "x50": float(out["x50"]),
+            "Reference_x50": ref["x50"],
+            "Objective_match": bool(np.isclose(
+                out["objective"], ref["objective"], rtol=rtol, atol=atol
+            )),
+            "Parameters_match": bool(np.allclose(
+                theta, ref["theta"], rtol=rtol, atol=atol
+            )),
+            "x50_match": bool(np.isclose(
+                out["x50"], ref["x50"], rtol=rtol, atol=atol
+            )),
+        })
+    return pd.DataFrame(rows)
+
+
+def print_ci_diagnostics(ci_res):
+    for key, name in (("orig", "FULL"), ("trim", "TRIM")):
+        out = ci_res[key]
+
+        print(f"\n{name}")
+        print("-" * len(name))
+        print(f"Conditional negative log-posterior: {out['objective']:.10g}")
+
+        hd = out["hessian_diagnostics"]
+        if hd:
+            print("Original Hessian positive definite:", hd["positive_definite"])
+            print("Hessian minimum eigenvalue:", hd["minimum_eigenvalue"])
+            print("Hessian condition number:", hd["condition_number"])
+            print(
+                "Original Hessian condition number:",
+                hd["original_condition_number"],
+            )
+            print("Hessian spectrally stabilized:", hd["stabilized"])
+            print("Wald/MCA covariance reliable:", hd["reliable"])
+            print("Eigenvalue floor:", hd["eigenvalue_floor"])
+            print(
+                "Maximum allowed stabilized condition:",
+                hd["maximum_allowed_condition"],
+            )
+
+        print(
+            "MAP parameters:",
+            dict(zip(PARAMETER_NAMES, out["theta_hat_vec"])),
+        )
+        print(f"x50={out['x50']:.8g}, s50={out['s50']:.8g}")
+
+        print("NPBS:", out["diagnostics_np"])
+        print("PBS:", out["diagnostics_pb"])
+        print("MCA:", out["diagnostics_mca"])
+
+
+def _percentile_or_nan(values, q):
+    values = np.asarray(values, float)
+    return float(np.percentile(values, q)) if values.size else np.nan
+
+
+def _ci_percentiles(out):
+    alpha = float(out.get("alpha_ci", 0.05))
+    return 100.0 * alpha / 2.0, 100.0 * (1.0 - alpha / 2.0)
+
+
+def _column_or_empty(values, j):
+    values = np.asarray(values, float)
+    return values[:, j] if values.ndim == 2 and values.shape[1] > j else []
+
+
+def make_parameter_ci_table(ci_res):
+    rows = []
+
+    for key, dataset in (("orig", "FULL"), ("trim", "TRIM")):
+        out = ci_res[key]
+        estimate = np.asarray(out["theta_hat_vec"], float)
+        qlo, qhi = _ci_percentiles(out)
+
+        for j, name in enumerate(PARAMETER_NAMES):
+            rows.append({
+                "Dataset": dataset,
+                "Parameter": name,
+                "Estimate": estimate[j],
+                "Wald_LL": out["wald_param_lo"][j],
+                "Wald_UL": out["wald_param_hi"][j],
+                "NPBS_LL": _percentile_or_nan(_column_or_empty(out["theta_np"], j), qlo),
+                "NPBS_UL": _percentile_or_nan(_column_or_empty(out["theta_np"], j), qhi),
+                "PBS_LL": _percentile_or_nan(_column_or_empty(out["theta_pb"], j), qlo),
+                "PBS_UL": _percentile_or_nan(_column_or_empty(out["theta_pb"], j), qhi),
+                "MCA_LL": _percentile_or_nan(
+                    out["theta_mca"][:, j] if out["theta_mca"].ndim == 2
+                    else [], qlo
+                ),
+                "MCA_UL": _percentile_or_nan(
+                    out["theta_mca"][:, j] if out["theta_mca"].ndim == 2
+                    else [], qhi
+                ),
+            })
+
+    return pd.DataFrame(rows)
+
+
+def make_derived_ci_table(ci_res):
+    rows = []
+
+    for key, dataset in (("orig", "FULL"), ("trim", "TRIM")):
+        out = ci_res[key]
+        qlo, qhi = _ci_percentiles(out)
+
+        for char, est, wlo, whi, npv, pbv in [
+            (
+                "x50",
+                out["x50"],
+                out["wald_x50_lo"],
+                out["wald_x50_hi"],
+                out["x50_np"],
+                out["x50_pb"],
+            ),
+            (
+                "s50",
+                out["s50"],
+                out["wald_s50_lo"],
+                out["wald_s50_hi"],
+                out["s50_np"],
+                out["s50_pb"],
+            ),
+        ]:
+            rows.append({
+                "Dataset": dataset,
+                "Characteristic": char,
+                "Estimate": est,
+                "Wald_LL": wlo,
+                "Wald_UL": whi,
+                "NPBS_LL": _percentile_or_nan(npv, qlo),
+                "NPBS_UL": _percentile_or_nan(npv, qhi),
+                "PBS_LL": _percentile_or_nan(pbv, qlo),
+                "PBS_UL": _percentile_or_nan(pbv, qhi),
+                "MCA_LL": _percentile_or_nan(
+                    out[f"{char}_mca"], qlo
+                ),
+                "MCA_UL": _percentile_or_nan(
+                    out[f"{char}_mca"], qhi
+                ),
+            })
+
+    return pd.DataFrame(rows)
+
+def smooth_ci_bounds(lower, upper, sigma=0.0):
+    """Optionally smooth CI boundaries for presentation only.
+
+    The empirical confidence limits stored in ``ci_res`` are not modified.
+    Numerical summaries and tables therefore continue to use the original
+    unsmoothed bootstrap distributions and confidence limits.
+    """
+    lower = np.asarray(lower, dtype=float)
+    upper = np.asarray(upper, dtype=float)
+
+    if lower.shape != upper.shape:
+        raise ValueError("Lower and upper CI boundaries must have equal shape.")
+    if lower.ndim != 1:
+        raise ValueError("CI boundaries must be one-dimensional arrays.")
+    if sigma <= 0:
+        return lower.copy(), upper.copy()
+
+    lower_smooth = gaussian_filter1d(lower, sigma=sigma, mode="nearest")
+    upper_smooth = gaussian_filter1d(upper, sigma=sigma, mode="nearest")
+
+    lower_smooth = np.clip(lower_smooth, 0.0, 1.0)
+    upper_smooth = np.clip(upper_smooth, 0.0, 1.0)
+
+    # Maintain a valid ordered confidence band after numerical smoothing.
+    lower_final = np.minimum(lower_smooth, upper_smooth)
+    upper_final = np.maximum(lower_smooth, upper_smooth)
+
+    return lower_final, upper_final
+
+
+def plot_bayesian_ci(
+    ci_res,
+    xmax=4.5,
+    figsize=(10, 4),
+    dpi=140,
+    smooth_sigma=0.0,
+    jitter=0.018,
+    jitter_seed=123,
+    band_support="observed",
+):
+    """Plot Bayesian risk functions and confidence bands.
+
+    Empirical boundaries are shown without smoothing by default. They are
+    smoothed for visualization only when
+    ``smooth_sigma`` is positive. The original empirical boundaries in
+    ``ci_res`` remain unchanged and continue to support all calculations.
+    Set ``smooth_sigma=0`` to display the original unsmoothed boundaries.
+    With ``band_support='observed'`` (default), all bands are displayed only
+    between the smallest and largest observed biomarker values in each panel;
+    use ``band_support='grid'`` to display bands over the entire model grid.
+    """
+    fig, axes = plt.subplots(
+        1,
+        2,
+        figsize=figsize,
+        dpi=dpi,
+        sharey=True,
+    )
+    alpha_plot = float(ci_res["orig"].get("alpha_ci", 0.05))
+    ci_level = 100.0 * (1.0 - alpha_plot)
+    ci_text = f"{ci_level:g}%"
+
+    # Colours corresponding to the previous figure
+    colors = {
+        "wald": "#138A24",   # green
+        "npbs": "#173BFF",   # blue
+        "pbs":  "#00CFE3",   # cyan
+        "mca":  "#B23AEE",   # purple
+        "nc":   "#7479FF",   # periwinkle
+        "ae":   "#FFBE63",   # orange
+    }
+
+    rng = np.random.default_rng(jitter_seed)
+
+    for ax, key, x_key, y_key, panel_label in zip(
+        axes,
+        ("orig", "trim"),
+        ("X_orig", "X_trim"),
+        ("y_orig", "y_trim"),
+        ("A", "B"),
+    ):
+        out = ci_res[key]
+        xg = ci_res["x_grid"]
+
+        # Observed samples with small vertical jitter to prevent overlap.
+        x_obs = np.asarray(ci_res[x_key])
+        y_obs = np.asarray(ci_res[y_key])
+        if band_support == "observed":
+            band_mask = (xg >= float(x_obs.min())) & (xg <= float(x_obs.max()))
+        elif band_support == "grid":
+            band_mask = np.ones(xg.shape, dtype=bool)
+        else:
+            raise ValueError("band_support must be 'observed' or 'grid'.")
+        x_band = xg[band_mask]
+        y_jittered = y_obs + rng.uniform(-jitter, jitter, size=y_obs.size)
+        ax.scatter(
+            x_obs[y_obs == 0],
+            y_jittered[y_obs == 0],
+            s=22,
+            color=colors["nc"],
+            alpha=0.72,
+            edgecolors="none",
+            zorder=7,
+        )
+        ax.scatter(
+            x_obs[y_obs == 1],
+            y_jittered[y_obs == 1],
+            s=25,
+            color=colors["ae"],
+            alpha=0.90,
+            edgecolors="none",
+            zorder=8,
+        )
+
+        # Fitted risk function
+        ax.plot(
+            xg,
+            out["pmap"],
+            color="black",
+            lw=2.2,
+            label="Fitted risk function",
+            zorder=5,
+        )
+
+        # Wald confidence band
+        if out["wald_available"]:
+            ax.fill_between(
+                x_band,
+                out["wald_lo"][band_mask],
+                out["wald_hi"][band_mask],
+                color=colors["wald"],
+                alpha=0.16,
+                label=f"Wald {ci_text} CI",
+                zorder=1,
+            )
+            ax.plot(
+                x_band,
+                out["wald_lo"][band_mask],
+                color=colors["wald"],
+                ls="-.",
+                lw=1.4,
+                zorder=3,
+            )
+            ax.plot(
+                x_band,
+                out["wald_hi"][band_mask],
+                color=colors["wald"],
+                ls="-.",
+                lw=1.4,
+                zorder=3,
+            )
+
+        # Nonparametric pairs bootstrap band
+        if out["np_lo"] is not None:
+            np_lo_plot, np_hi_plot = smooth_ci_bounds(
+                out["np_lo"],
+                out["np_hi"],
+                sigma=smooth_sigma,
+            )
+            ax.fill_between(
+                x_band,
+                np_lo_plot[band_mask],
+                np_hi_plot[band_mask],
+                color=colors["npbs"],
+                alpha=0.14,
+                label=f"NPBS {ci_text} CI",
+                zorder=1,
+            )
+            ax.plot(
+                x_band,
+                np_lo_plot[band_mask],
+                color=colors["npbs"],
+                ls=":",
+                lw=1.4,
+                zorder=3,
+            )
+            ax.plot(
+                x_band,
+                np_hi_plot[band_mask],
+                color=colors["npbs"],
+                ls=":",
+                lw=1.4,
+                zorder=3,
+            )
+
+        # Parametric bootstrap band
+        if out["pb_lo"] is not None:
+            pb_lo_plot, pb_hi_plot = smooth_ci_bounds(
+                out["pb_lo"],
+                out["pb_hi"],
+                sigma=smooth_sigma,
+            )
+            ax.fill_between(
+                x_band,
+                pb_lo_plot[band_mask],
+                pb_hi_plot[band_mask],
+                color=colors["pbs"],
+                alpha=0.14,
+                label=f"PBS {ci_text} CI",
+                zorder=1,
+            )
+            ax.plot(
+                x_band,
+                pb_lo_plot[band_mask],
+                color=colors["pbs"],
+                ls="--",
+                lw=1.6,
+                zorder=3,
+            )
+            ax.plot(
+                x_band,
+                pb_hi_plot[band_mask],
+                color=colors["pbs"],
+                ls="--",
+                lw=1.6,
+                zorder=3,
+            )
+
+        # Strict local-Gaussian Monte Carlo approximation
+        if out["mca_lo"] is not None:
+            mca_lo_plot, mca_hi_plot = smooth_ci_bounds(
+                out["mca_lo"], out["mca_hi"], sigma=smooth_sigma
+            )
+            ax.fill_between(
+                x_band, mca_lo_plot[band_mask], mca_hi_plot[band_mask],
+                color=colors["mca"], alpha=0.10, zorder=1,
+            )
+            ax.plot(
+                x_band, mca_lo_plot[band_mask], color=colors["mca"],
+                ls=(0, (5, 2, 1, 2)), lw=1.5, zorder=3,
+            )
+            ax.plot(
+                x_band, mca_hi_plot[band_mask], color=colors["mca"],
+                ls=(0, (5, 2, 1, 2)), lw=1.5, zorder=3,
+            )
+
+        ax.set_xlim(xg.min(), xmax)
+        ax.set_ylim(-0.05, 1.05)
+        ax.set_xlabel(r"$X$")
+        ax.grid(False)
+        ax.text(
+            0.045,
+            0.955,
+            panel_label,
+            transform=ax.transAxes,
+            ha="left",
+            va="top",
+            fontsize=14,
+            fontweight="normal",
+            zorder=10,
+        )
+
+    axes[0].set_ylabel(r"$P(\mathrm{AE}\mid X=x)$")
+
+    # Complete legend inside the lower-right corner of panel B.
+    legend_handles = [
+        Line2D(
+            [0], [0],
+            marker="o",
+            linestyle="none",
+            markerfacecolor=colors["nc"],
+            markeredgecolor="none",
+            markersize=7,
+            label="data: NC",
+        ),
+        Line2D(
+            [0], [0],
+            marker="o",
+            linestyle="none",
+            markerfacecolor=colors["ae"],
+            markeredgecolor="none",
+            markersize=7,
+            label="data: AE",
+        ),
+        Line2D(
+            [0], [0],
+            color="black",
+            ls="-",
+            lw=2.2,
+            label="fit",
+        ),
+    ]
+
+    if any(ci_res[key]["wald_available"] for key in ("orig", "trim")):
+        legend_handles.append(Line2D(
+            [0], [0], color=colors["wald"], ls="-.", lw=1.8,
+            label=f"CI: Wald {ci_text}",
+        ))
+    if any(ci_res[key]["np_lo"] is not None for key in ("orig", "trim")):
+        legend_handles.append(Line2D(
+            [0], [0], color=colors["npbs"], ls=":", lw=1.8,
+            label=f"CI: NPBS {ci_text}",
+        ))
+    if any(ci_res[key]["pb_lo"] is not None for key in ("orig", "trim")):
+        legend_handles.append(Line2D(
+            [0], [0], color=colors["pbs"], ls="--", lw=2.0,
+            label=f"CI: PBS {ci_text}",
+        ))
+    if any(ci_res[key]["mca_lo"] is not None for key in ("orig", "trim")):
+        legend_handles.append(Line2D(
+            [0], [0], color=colors["mca"],
+            ls=(0, (5, 2, 1, 2)), lw=1.8,
+            label=f"CI: MCA {ci_text}",
+        ))
+
+    axes[1].legend(
+        handles=legend_handles,
+        loc="lower right",
+        frameon=True,
+        framealpha=0.95,
+        fontsize=9,
+    )
+
+    plt.tight_layout()
+
+    return fig, axes
+
+# ============================================================

organized_uncertainty_analysis/bayesian/data_fit_gof.py

@@ -0,0 +1,56 @@
+"""Data preparation, constrained MAP fitting, prediction, and fit diagnostics."""
+
+import numpy as np
+
+from .core import (
+    load_xy,
+    make_trimmed_dataset,
+    sigmoid,
+    softplus,
+    theta_max,
+    unpack,
+    dE_full,
+    P_with,
+    make_priors,
+    init_phi,
+    neg_post,
+    fit_bayes,
+    x_at_p,
+    slope_at_x,
+)
+
+
+def goodness_of_fit(X, y, theta_hat, threshold=0.5):
+    """Return conditional Bernoulli fit measures for a fitted CB model."""
+    X = np.asarray(X, float).ravel()
+    y = np.asarray(y, int).ravel()
+    p = np.clip(np.asarray(P_with(theta_hat, X), float), 1e-12, 1.0 - 1e-12)
+    pred = (p >= threshold).astype(int)
+    log_loss = -float(np.mean(y * np.log(p) + (1 - y) * np.log1p(-p)))
+    return {
+        "n": int(y.size),
+        "events": int(y.sum()),
+        "log_loss": log_loss,
+        "brier_score": float(np.mean((y - p) ** 2)),
+        "accuracy": float(np.mean(pred == y)),
+        "sensitivity": float(np.mean(pred[y == 1] == 1)) if np.any(y == 1) else np.nan,
+        "specificity": float(np.mean(pred[y == 0] == 0)) if np.any(y == 0) else np.nan,
+    }
+
+
+def fit_full_trim(percentile=95, **fit_kwargs):
+    """Load, trim, and fit the FULL and TRIM constrained Bayesian models."""
+    X, y = load_xy(perc=percentile)
+    ds = make_trimmed_dataset(X, y)
+    result = {"data": ds}
+    for key, x_key, y_key in (
+        ("FULL", "X_orig", "y_orig"),
+        ("TRIM", "X_trim", "y_trim"),
+    ):
+        theta, optimizer = fit_bayes(ds[x_key], ds[y_key], **fit_kwargs)
+        result[key] = {
+            "theta": theta,
+            "optimizer": optimizer,
+            "gof": goodness_of_fit(ds[x_key], ds[y_key], theta),
+        }
+    return result

organized_uncertainty_analysis/bayesian/elasticity.py

@@ -0,0 +1,75 @@
+"""Numerical elasticities of Bayesian x50 and s50 to scientific parameters."""
+
+import numpy as np
+import pandas as pd
+import matplotlib.pyplot as plt
+
+from .core import P_with, slope_at_x, theta_max, x_at_p
+
+PARAMETER_NAMES = ("omega", "a", "b", "s", "k", "vartheta")
+
+
+def _scientific_vector(theta_hat):
+    return np.asarray(theta_hat[:6], float)
+
+
+def _as_theta(values):
+    omega, a, b, s, k, vartheta = map(float, values)
+    cap = theta_max(a, b, k, s)
+    if not (0 < omega < 1 and a > k > 0 and b > 0 and s > 0 and 0 < vartheta < cap):
+        raise ValueError("Perturbed parameter vector violates model constraints.")
+    return omega, a, b, s, k, vartheta, cap
+
+
+def elasticity_x50_s50(theta_hat, relative_step=1e-4):
+    """Return dimensionless local elasticities using central perturbations."""
+    base = _scientific_vector(theta_hat)
+    base_theta = _as_theta(base)
+    x0 = x_at_p(base_theta)
+    s0 = slope_at_x(base_theta, x0)
+    rows = []
+    for j, name in enumerate(PARAMETER_NAMES):
+        step = relative_step * max(abs(base[j]), 1e-8)
+        plus, minus = base.copy(), base.copy()
+        plus[j] += step
+        minus[j] -= step
+        try:
+            tp, tm = _as_theta(plus), _as_theta(minus)
+            xp, xm = x_at_p(tp), x_at_p(tm)
+            sp, sm = slope_at_x(tp, xp), slope_at_x(tm, xm)
+            ex = (base[j] / x0) * (xp - xm) / (2.0 * step)
+            es = (base[j] / s0) * (sp - sm) / (2.0 * step)
+        except (ValueError, FloatingPointError):
+            ex = es = np.nan
+        rows.append({"Parameter": name, "Elasticity_x50": ex, "Elasticity_s50": es})
+    return pd.DataFrame(rows)
+
+
+def elasticity_full_trim(fit_result, relative_step=1e-4):
+    frames = []
+    for dataset in ("FULL", "TRIM"):
+        frame = elasticity_x50_s50(fit_result[dataset]["theta"], relative_step)
+        frame.insert(0, "Dataset", dataset)
+        frames.append(frame)
+    return pd.concat(frames, ignore_index=True)
+
+
+def plot_combined_elasticity(table):
+    """Plot all Bayesian parameter elasticities in one two-panel figure."""
+    parameter_order = list(PARAMETER_NAMES)
+    display_labels = [r"$\pi$", r"$a$", r"$b$", r"$s$", r"$k$", r"$\vartheta$"]
+    x = np.arange(len(parameter_order))
+    width = 0.36
+    fig, axes = plt.subplots(1, 2, figsize=(11, 4.2), dpi=180)
+    for offset, dataset in zip((-width / 2, width / 2), ("FULL", "TRIM")):
+        block = table.set_index(["Dataset", "Parameter"]).loc[dataset].reindex(parameter_order)
+        axes[0].bar(x + offset, block["Elasticity_x50"].abs(), width=width, label=dataset)
+        axes[1].bar(x + offset, block["Elasticity_s50"].abs(), width=width, label=dataset)
+    for label, axis in zip(("A", "B"), axes):
+        axis.set_xticks(x, display_labels)
+        axis.set_ylabel("Absolute elasticity")
+        axis.text(0.02, 0.97, label, transform=axis.transAxes, ha="left", va="top", fontsize=15)
+        axis.grid(alpha=0.25, axis="y")
+    axes[0].legend(frameon=True, fontsize=9, loc="upper left")
+    fig.tight_layout()
+    return fig, axes

organized_uncertainty_analysis/bayesian/noise_core.py

@@ -0,0 +1,457 @@
+# bayesian_noise.py
+# ============================================================
+# Bayesian noise propagation on RAW X
+# Reference location and Δ widths are evaluated at exact clean-fit x50
+# Function-only module for notebook use
+# ============================================================
+
+import numpy as np
+import matplotlib.pyplot as plt
+from scipy.optimize import brentq
+
+from .core import load_xy, fit_bayes, P_with, make_trimmed_dataset
+
+# ---------------- Defaults ----------------
+XMAX = 5.0
+GRID_N = 1000
+
+SIGMA_MULT = 0.129
+SIGMA_ADD = 0.144
+
+N_REFIT = 150
+N_TTA = 300
+SEED = 1234
+
+CI_LEVEL = 0.95
+ALPHA = 1.0 - CI_LEVEL
+Q_LO, Q_MD, Q_HI = ALPHA / 2.0, 0.5, 1.0 - ALPHA / 2.0
+
+USE_PRIOR_P = True
+PRIOR_R = (1.05, 1.05)
+TAU = 25.0
+
+plt.rcParams["legend.frameon"] = False
+plt.rcParams["axes.titleweight"] = "normal"
+plt.rcParams["axes.labelweight"] = "normal"
+
+
+# ============================================================
+# 1) DATA
+# ============================================================
+
+def load_original(
+    perc=95,
+    suv_path="suv_percentilesSLOthenUWM.mat",
+    flags_path="flags_combined.mat",
+):
+    return load_xy(perc=perc, suv_path=suv_path, flags_path=flags_path)
+
+
+def load_trimmed(
+    perc=95,
+    suv_path="suv_percentilesSLOthenUWM.mat",
+    flags_path="flags_combined.mat",
+    value_to_drop=2.48122597,
+    tol=1e-3,
+):
+    X, y = load_xy(perc=perc, suv_path=suv_path, flags_path=flags_path)
+    ds = make_trimmed_dataset(X, y, value_to_drop=value_to_drop, tol=tol)
+    return ds["X_trim"], ds["y_trim"]
+
+
+# ============================================================
+# 2) FIT + X50
+# ============================================================
+
+def fit_once(X, y, rng, use_prior_p=USE_PRIOR_P, prior_r=PRIOR_R, tau=TAU):
+    theta, res = fit_bayes(
+        X,
+        y,
+        seed=int(rng.integers(0, 10_000_000)),
+        use_prior_p=use_prior_p,
+        prior_r=prior_r,
+        tau=tau,
+    )
+    return theta, res
+
+
+def x_at_p(theta_hat, p_target=0.5, lo=1e-6, hi=6.0, hi_max=100.0):
+    """
+    Exact root solve for P(AE|x)=p_target.
+    """
+    f = lambda x: P_with(theta_hat, x) - p_target
+    fa, fb = f(lo), f(hi)
+
+    while np.isfinite(fa) and np.isfinite(fb) and fa * fb > 0 and hi < hi_max:
+        hi *= 2.0
+        fb = f(hi)
+
+    if (not np.isfinite(fa)) or (not np.isfinite(fb)) or fa * fb > 0:
+        return np.nan
+
+    try:
+        return float(brentq(f, lo, hi))
+    except Exception:
+        return np.nan
+
+
+# ============================================================
+# 3) NOISE
+# ============================================================
+
+def add_noise_mult(X, sigma, rng):
+    X = np.asarray(X, float)
+    return np.clip(X * np.exp(rng.normal(0, sigma, size=X.shape)), 1e-12, None)
+
+
+def add_noise_add(X, sigma, rng):
+    X = np.asarray(X, float)
+    return np.clip(X + rng.normal(0, sigma, size=X.shape), 1e-12, None)
+
+
+# ============================================================
+# 4) BAND HELPERS
+# ============================================================
+
+def monotone_nondec(y):
+    y = np.asarray(y, float)
+    return np.maximum.accumulate(np.clip(y, 0, 1))
+
+
+def band_quantiles(curves, q_lo=Q_LO, q_md=Q_MD, q_hi=Q_HI):
+    C = np.vstack(curves)
+    ql = monotone_nondec(np.quantile(C, q_lo, axis=0))
+    qm = monotone_nondec(np.quantile(C, q_md, axis=0))
+    qh = monotone_nondec(np.quantile(C, q_hi, axis=0))
+    return ql, qm, qh
+
+
+def delta_width_at_x(lo, hi, xc, x0):
+    if not np.isfinite(x0):
+        return np.nan
+    lo_x = float(np.interp(x0, xc, lo))
+    hi_x = float(np.interp(x0, xc, hi))
+    return hi_x - lo_x
+
+
+# ============================================================
+# 5) CORE ANALYSIS
+# ============================================================
+
+def build_bands_for_dataset(
+    X,
+    y,
+    sigma_mult=SIGMA_MULT,
+    sigma_add=SIGMA_ADD,
+    x_max=XMAX,
+    grid_n=GRID_N,
+    n_refit=N_REFIT,
+    n_tta=N_TTA,
+    seed=SEED,
+    use_prior_p=USE_PRIOR_P,
+    prior_r=PRIOR_R,
+    tau=TAU,
+):
+    X = np.asarray(X, float)
+    y = np.asarray(y, int)
+
+    rng = np.random.default_rng(seed)
+    xc = np.linspace(1e-12, x_max, grid_n)
+
+    theta_clean, res_clean = fit_once(
+        X, y, rng,
+        use_prior_p=use_prior_p,
+        prior_r=prior_r,
+        tau=tau,
+    )
+    clean_curve = P_with(theta_clean, xc)
+    x50 = x_at_p(theta_clean, p_target=0.5, lo=1e-6, hi=max(6.0, x_max))
+
+    # multiplicative: refit
+    curves_refit_m = []
+    for _ in range(n_refit):
+        Xn = add_noise_mult(X, sigma_mult, rng)
+        thetab, resb = fit_once(
+            Xn, y, rng,
+            use_prior_p=use_prior_p,
+            prior_r=prior_r,
+            tau=tau
+        )
+        if resb.success and np.isfinite(resb.fun):
+            curves_refit_m.append(P_with(thetab, xc))
+    if not curves_refit_m:
+        raise RuntimeError("No successful multiplicative-refit curves.")
+    lo_rm, md_rm, hi_rm = band_quantiles(curves_refit_m)
+
+    # multiplicative: TTA
+    curves_tta_m = []
+    for _ in range(n_tta):
+        xc_n = np.clip(xc * np.exp(rng.normal(0, sigma_mult, size=xc.size)), 1e-12, None)
+        curves_tta_m.append(P_with(theta_clean, xc_n))
+    lo_tm, md_tm, hi_tm = band_quantiles(curves_tta_m)
+
+    # additive: refit
+    curves_refit_a = []
+    for _ in range(n_refit):
+        Xn = add_noise_add(X, sigma_add, rng)
+        thetab, resb = fit_once(
+            Xn, y, rng,
+            use_prior_p=use_prior_p,
+            prior_r=prior_r,
+            tau=tau
+        )
+        if resb.success and np.isfinite(resb.fun):
+            curves_refit_a.append(P_with(thetab, xc))
+    if not curves_refit_a:
+        raise RuntimeError("No successful additive-refit curves.")
+    lo_ra, md_ra, hi_ra = band_quantiles(curves_refit_a)
+
+    # additive: TTA
+    curves_tta_a = []
+    for _ in range(n_tta):
+        xc_n = np.clip(xc + rng.normal(0, sigma_add, size=xc.size), 1e-12, None)
+        curves_tta_a.append(P_with(theta_clean, xc_n))
+    lo_ta, md_ta, hi_ta = band_quantiles(curves_tta_a)
+
+    return {
+        "X": X.copy(),
+        "y": y.copy(),
+        "xc": xc,
+        "theta_clean": theta_clean,
+        "fit_success": bool(res_clean.success),
+        "clean_curve": clean_curve,
+        "x50": x50,
+        "mult": {
+            "sigma": sigma_mult,
+            "refit": (lo_rm, md_rm, hi_rm),
+            "tta": (lo_tm, md_tm, hi_tm),
+            "D_refit": delta_width_at_x(lo_rm, hi_rm, xc, x50),
+            "D_tta": delta_width_at_x(lo_tm, hi_tm, xc, x50),
+            "n_refit_success": len(curves_refit_m),
+            "n_tta": len(curves_tta_m),
+        },
+        "add": {
+            "sigma": sigma_add,
+            "refit": (lo_ra, md_ra, hi_ra),
+            "tta": (lo_ta, md_ta, hi_ta),
+            "D_refit": delta_width_at_x(lo_ra, hi_ra, xc, x50),
+            "D_tta": delta_width_at_x(lo_ta, hi_ta, xc, x50),
+            "n_refit_success": len(curves_refit_a),
+            "n_tta": len(curves_tta_a),
+        },
+    }
+
+
+def run_noise_analysis(
+    perc=95,
+    suv_path="suv_percentilesSLOthenUWM.mat",
+    flags_path="flags_combined.mat",
+    value_to_drop=2.48122597,
+    tol=1e-3,
+    sigma_mult=SIGMA_MULT,
+    sigma_add=SIGMA_ADD,
+    x_max=XMAX,
+    grid_n=GRID_N,
+    n_refit=N_REFIT,
+    n_tta=N_TTA,
+    seed=SEED,
+    use_prior_p=USE_PRIOR_P,
+    prior_r=PRIOR_R,
+    tau=TAU,
+):
+    X_full, y_full = load_original(
+        perc=perc, suv_path=suv_path, flags_path=flags_path
+    )
+    X_trim, y_trim = load_trimmed(
+        perc=perc, suv_path=suv_path, flags_path=flags_path,
+        value_to_drop=value_to_drop, tol=tol
+    )
+
+    full_res = build_bands_for_dataset(
+        X_full, y_full,
+        sigma_mult=sigma_mult, sigma_add=sigma_add,
+        x_max=x_max, grid_n=grid_n,
+        n_refit=n_refit, n_tta=n_tta,
+        seed=seed,
+        use_prior_p=use_prior_p, prior_r=prior_r, tau=tau,
+    )
+    trim_res = build_bands_for_dataset(
+        X_trim, y_trim,
+        sigma_mult=sigma_mult, sigma_add=sigma_add,
+        x_max=x_max, grid_n=grid_n,
+        n_refit=n_refit, n_tta=n_tta,
+        seed=seed + 100,
+        use_prior_p=use_prior_p, prior_r=prior_r, tau=tau,
+    )
+
+    return {"full": full_res, "trim": trim_res}
+
+
+# ============================================================
+# 6) SUMMARY TABLE
+# ============================================================
+
+def make_noise_summary_table(noise_res):
+    rows = []
+    for dataset_name, block in [("FULL", noise_res["full"]), ("TRIM", noise_res["trim"])]:
+        for noise_name, key in [("multiplicative", "mult"), ("additive", "add")]:
+            rows.append({
+                "Dataset": dataset_name,
+                "NoiseType": noise_name,
+                "Sigma": float(block[key]["sigma"]),
+                "x50": float(block["x50"]),
+                "Delta_refit_at_x50": float(block[key]["D_refit"]),
+                "Delta_tta_at_x50": float(block[key]["D_tta"]),
+                "N_refit_success": int(block[key]["n_refit_success"]),
+                "N_tta": int(block[key]["n_tta"]),
+            })
+    import pandas as pd
+    return pd.DataFrame(rows)
+
+
+# ============================================================
+# 7) PLOTTING
+# ============================================================
+
+def plot_4panels(
+    full_res,
+    trim_res,
+    save_prefix="noise_cb_raw_4panels_sigma129_0144_x50",
+    x_max=XMAX,
+    sigma_mult=SIGMA_MULT,
+    sigma_add=SIGMA_ADD,
+):
+    import numpy as np
+    import matplotlib.pyplot as plt
+
+    fig, axs = plt.subplots(
+        2, 2, figsize=(12.5, 7.5), dpi=160, sharex=True, sharey=True
+    )
+
+    COL = {"mult": "#1f78b4", "add": "#ff7f00"}
+    ALP = {"refit": 0.25, "tta": 0.12}
+
+    COL_NC = "#4C78A8"
+    COL_AE = "#F58518"
+
+    def draw_panel(ax, res, mode, letter, dataset_label):
+        xc = res["xc"]
+        clean = res["clean_curve"]
+        x50 = float(res["x50"])
+
+        X = np.asarray(res["X"], float)
+        y = np.asarray(res["y"], int)
+
+        lo_r, _, hi_r = res[mode]["refit"]
+        lo_t, _, hi_t = res[mode]["tta"]
+        Dref = res[mode]["D_refit"]
+        Dtta = res[mode]["D_tta"]
+
+        # data points (no jitter)
+        ax.scatter(
+            X[y == 0], y[y == 0],
+            s=14, color=COL_NC, alpha=0.45,
+            edgecolors="none", zorder=5
+        )
+        ax.scatter(
+            X[y == 1], y[y == 1],
+            s=14, color=COL_AE, alpha=0.65,
+            edgecolors="none", zorder=5
+        )
+
+        # clean fit
+        ax.plot(xc, clean, color="k", lw=2.6, zorder=4)
+
+        # uncertainty bands
+        ax.fill_between(xc, lo_r, hi_r, color=COL[mode], alpha=ALP["refit"], zorder=1)
+        ax.fill_between(xc, lo_t, hi_t, color=COL[mode], alpha=ALP["tta"], zorder=0)
+
+        # x50 line
+        if np.isfinite(x50):
+            ax.axvline(x50, color="#666666", ls="--", lw=1.2, alpha=0.9, zorder=3)
+
+        # panel label
+        ax.text(
+            0.03, 0.97, letter,
+            transform=ax.transAxes,
+            ha="left", va="top",
+            fontsize=15
+        )
+
+        # info box
+        info_txt = (
+            f"{dataset_label}\n"
+            f"$x_{{50}}$={x50:.2f}\n"
+            f"$\\Delta r$={Dref:.2f}  $\\Delta t$={Dtta:.2f}"
+        )
+        ax.text(
+            0.02, 0.14,
+            info_txt,
+            transform=ax.transAxes,
+            ha="left", va="bottom",
+            fontsize=10,
+            color="#222",
+            bbox=dict(
+                facecolor="white",
+                edgecolor=COL[mode],
+                boxstyle="square,pad=0.25",
+                lw=0.9,
+                alpha=0.95
+            )
+        )
+
+        # axes
+        ax.set_xlim(0, x_max)
+        ax.set_ylim(-0.05, 1.05)
+        ax.grid(alpha=0.25)
+        ax.tick_params(axis="both", labelsize=10)
+
+    draw_panel(axs[0, 0], full_res, "mult", "A", "FULL")
+    draw_panel(axs[0, 1], full_res, "add",  "B", "FULL")
+    draw_panel(axs[1, 0], trim_res, "mult", "C", "TRIM")
+    draw_panel(axs[1, 1], trim_res, "add",  "D", "TRIM")
+
+    axs[1, 0].set_xlabel(r"$X$", fontsize=12)
+    axs[1, 1].set_xlabel(r"$X$", fontsize=12)
+    axs[0, 0].set_ylabel(r"$P(\mathrm{AE}\mid X=x)$", fontsize=12)
+    axs[1, 0].set_ylabel(r"$P(\mathrm{AE}\mid X=x)$", fontsize=12)
+
+    handles = [
+        plt.Line2D([0], [0], marker="o", linestyle="None",
+                   markerfacecolor=COL_NC, markeredgecolor="none",
+                   markersize=6, label="NC data"),
+        plt.Line2D([0], [0], marker="o", linestyle="None",
+                   markerfacecolor=COL_AE, markeredgecolor="none",
+                   markersize=6, label="AE data"),
+        plt.Line2D([0], [0], color="k", lw=2.6, label="Initial fit"),
+        plt.Rectangle((0, 0), 1, 1, facecolor=COL["mult"], alpha=ALP["refit"],
+                      label=f"refit band, mult σ={sigma_mult:.3f}"),
+        plt.Rectangle((0, 0), 1, 1, facecolor=COL["mult"], alpha=ALP["tta"],
+                      label=f"fixe-model band, mult σ={sigma_mult:.3f}"),
+        plt.Rectangle((0, 0), 1, 1, facecolor=COL["add"], alpha=ALP["refit"],
+                      label=f"refit band, add σ={sigma_add:.3f}"),
+        plt.Rectangle((0, 0), 1, 1, facecolor=COL["add"], alpha=ALP["tta"],
+                      label=f"fixed-model band, add σ={sigma_add:.3f}"),
+        plt.Line2D([0], [0], color="#666666", lw=1.2, ls="--", label=r"$x_{50}$"),
+    ]
+
+    leg = axs[1, 1].legend(
+        handles=handles,
+        loc="lower right",
+        bbox_to_anchor=(0.97, 0.05),
+        fontsize=9,
+        frameon=True
+    )
+
+    frame = leg.get_frame()
+    frame.set_facecolor("white")
+    frame.set_edgecolor("#bdbdbd")
+    frame.set_linewidth(0.8)
+
+    plt.tight_layout()
+
+    if save_prefix is not None:
+        fig.savefig(f"{save_prefix}.png", dpi=300, bbox_inches="tight")
+        fig.savefig(f"{save_prefix}.pdf", bbox_inches="tight")
+
+    return fig, axs

organized_uncertainty_analysis/bayesian/noise_measurement.py

@@ -0,0 +1,16 @@
+"""Additive and multiplicative measurement-noise propagation."""
+
+from .noise_core import (
+    load_original,
+    load_trimmed,
+    fit_once,
+    x_at_p,
+    add_noise_mult,
+    add_noise_add,
+    band_quantiles,
+    delta_width_at_x,
+    build_bands_for_dataset,
+    run_noise_analysis,
+    make_noise_summary_table,
+    plot_4panels,
+)

organized_uncertainty_analysis/bayesian/notebooks/01_data_fit_gof.ipynb

@@ -0,0 +1,165 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "03daa2c8",
+   "metadata": {},
+   "source": [
+    "# Constrained Bayesian model: data, fitting, and goodness of fit\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "id": "09df5fc0",
+   "metadata": {
+    "execution": {
+     "iopub.execute_input": "2026-09-14T14:44:31.677158Z",
+     "iopub.status.busy": "2026-09-14T14:44:31.675138Z",
+     "iopub.status.idle": "2026-09-14T14:44:41.667953Z",
+     "shell.execute_reply": "2026-09-14T14:44:41.667061Z"
+    }
+   },
+   "outputs": [],
+   "source": [
+    "from pathlib import Path\n",
+    "import sys\n",
+    "\n",
+    "PROJECT_ROOT = Path.cwd().resolve()\n",
+    "while not (PROJECT_ROOT / 'data.py').exists():\n",
+    "    if PROJECT_ROOT.parent == PROJECT_ROOT:\n",
+    "        raise FileNotFoundError('Open this notebook from inside organized_uncertainty_analysis.')\n",
+    "    PROJECT_ROOT = PROJECT_ROOT.parent\n",
+    "if str(PROJECT_ROOT.parent) not in sys.path:\n",
+    "    sys.path.insert(0, str(PROJECT_ROOT.parent))\n",
+    "\n",
+    "import os\n",
+    "os.chdir(PROJECT_ROOT)\n",
+    "from organized_uncertainty_analysis.bayesian import data_fit_gof as fit\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "id": "7f289ee0",
+   "metadata": {
+    "execution": {
+     "iopub.execute_input": "2026-09-14T14:44:41.677414Z",
+     "iopub.status.busy": "2026-09-14T14:44:41.677414Z",
+     "iopub.status.idle": "2026-09-14T14:44:44.496970Z",
+     "shell.execute_reply": "2026-09-14T14:44:44.495211Z"
+    }
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Loading SUV from: .\\suv_percentilesSLOthenUWM.mat\n",
+      "Loading FLAGS from: .\\flags_combined.mat\n"
+     ]
+    },
+    {
+     "data": {
+      "text/html": [
+       "<div>\n",
+       "<style scoped>\n",
+       "    .dataframe tbody tr th:only-of-type {\n",
+       "        vertical-align: middle;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe tbody tr th {\n",
+       "        vertical-align: top;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe thead th {\n",
+       "        text-align: right;\n",
+       "    }\n",
+       "</style>\n",
+       "<table border=\"1\" class=\"dataframe\">\n",
+       "  <thead>\n",
+       "    <tr style=\"text-align: right;\">\n",
+       "      <th></th>\n",
+       "      <th>Dataset</th>\n",
+       "      <th>n</th>\n",
+       "      <th>events</th>\n",
+       "      <th>log_loss</th>\n",
+       "      <th>brier_score</th>\n",
+       "      <th>accuracy</th>\n",
+       "      <th>sensitivity</th>\n",
+       "      <th>specificity</th>\n",
+       "    </tr>\n",
+       "  </thead>\n",
+       "  <tbody>\n",
+       "    <tr>\n",
+       "      <th>0</th>\n",
+       "      <td>FULL</td>\n",
+       "      <td>58</td>\n",
+       "      <td>5</td>\n",
+       "      <td>0.080578</td>\n",
+       "      <td>0.027564</td>\n",
+       "      <td>0.965517</td>\n",
+       "      <td>0.8</td>\n",
+       "      <td>0.981132</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>1</th>\n",
+       "      <td>TRIM</td>\n",
+       "      <td>57</td>\n",
+       "      <td>5</td>\n",
+       "      <td>0.045645</td>\n",
+       "      <td>0.016372</td>\n",
+       "      <td>0.964912</td>\n",
+       "      <td>0.8</td>\n",
+       "      <td>0.980769</td>\n",
+       "    </tr>\n",
+       "  </tbody>\n",
+       "</table>\n",
+       "</div>"
+      ],
+      "text/plain": [
+       "  Dataset   n  events  log_loss  brier_score  accuracy  sensitivity  \\\n",
+       "0    FULL  58       5  0.080578     0.027564  0.965517          0.8   \n",
+       "1    TRIM  57       5  0.045645     0.016372  0.964912          0.8   \n",
+       "\n",
+       "   specificity  \n",
+       "0     0.981132  \n",
+       "1     0.980769  "
+      ]
+     },
+     "execution_count": 2,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "import pandas as pd\n",
+    "fit_result = fit.fit_full_trim(seed=123)\n",
+    "gof_table = pd.DataFrame([{'Dataset': name, **fit_result[name]['gof']} for name in ('FULL', 'TRIM')])\n",
+    "gof_table.to_csv(PROJECT_ROOT / 'outputs' / 'bayesian_goodness_of_fit.csv', index=False)\n",
+    "gof_table\n"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.12.7"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}

organized_uncertainty_analysis/data.py

@@ -0,0 +1,55 @@
+# data.py
+import numpy as np
+
+"""
+LUNG data extraction (with NaN filtering)
+
+This file does one job:
+1) Read lung SUV percentile data from `suv_dict`
+2) Build one feature per patient:
+      x[i] = max value (ignoring NaNs) of the chosen percentile for patient i
+3) Read lung labels from `flags_dict`:
+      y[i] = 0 (NC) or 1 (AE)
+4) Remove patients where x is NaN (and keep y aligned)
+
+Important:
+- Logistic regression (sklearn) cannot use NaNs in X.
+- So we filter NaNs here to always return clean data.
+
+Inputs:
+- perc: percentile number (1..100), e.g. 95
+- suv_dict: dict loaded from the SUV .mat file
+- flags_dict: dict loaded from the flags .mat file
+- nr_patient: number of patients to use (default 58)
+
+Outputs:
+- x: 1D numpy array (NaNs removed)
+- y: 1D numpy array (aligned with x)
+"""
+
+
+def get_data(perc, suv_dict, flags_dict):
+    """
+    Extract SUV percentile feature and AE labels.
+
+    PERC = 95 -> uses column index 94
+    """
+
+    # SUV matrix: (patients × percentiles × organs)
+    suv = suv_dict["lung_SUVperc_COMBINED"]
+
+    # Flags: AE indicator
+    flags = flags_dict["flags"]
+
+    # We only use first 58 patients and column 3 for AE
+    y = flags[:58, 3].astype(int).ravel()
+
+    # Percentile index (95th -> column 94)
+    p_idx = perc - 1
+
+    # Extract feature: max over organs at that percentile
+    x = np.nanmax(suv[:58, :, p_idx], axis=1).astype(float)
+
+    # Remove NaNs
+    mask = np.isfinite(x)
+    return x[mask], y[mask]

organized_uncertainty_analysis/examples/bayesian_synthetic/README.md

@@ -0,0 +1,37 @@
+# Synthetic constrained Bayesian reproducibility example
+
+This example runs the constrained Bayesian workflow on generic positive `x`
+values and binary `y` outcomes. The predictor is not on the SUV scale and has
+no clinical interpretation. The example checks software execution and
+reproducibility; it is not statistical or clinical validation.
+
+The complete workflow can be run either as a script or as a clean notebook:
+
+```bash
+python examples/bayesian_synthetic/run_synthetic_bayesian.py
+```
+
+- `synthetic_bayesian_notebook.ipynb` runs data generation, model fitting and
+  goodness of fit, interval and band estimation, elasticity, and measurement
+  noise propagation.
+- `run_synthetic_bayesian.py` runs the same stages from the command line.
+
+The fixed random seed reproduces the same data and results. Generated tables
+and figures are written to `examples/bayesian_synthetic/outputs/`. Replication
+counts and the output directory can be changed through the environment
+variables defined near the top of the script.
+
+## MCA diagnostic
+
+`bayesian_mca_repeated_simulation.py` is a separate numerical diagnostic. It
+generates data under three controlled conditions and repeatedly evaluates the
+Monte Carlo approximation (MCA). The accompanying CSV files contain the
+replicate-level results and their summary; the two PDF files show the
+three-source diagnostic and representative pointwise bands.
+
+The diagnostic shows that MCA behavior depends on how strongly the data
+identify the constrained model parameters. MCA propagates a stabilized local
+Gaussian approximation around the MAP estimate. It is therefore retained as a
+local approximation and should not be interpreted as full posterior inference.
+Wide MCA intervals or bands are reported rather than tuned away. NPBS and PBS
+provide complementary refitting-based uncertainty assessments.

organized_uncertainty_analysis/examples/bayesian_synthetic/bayesian_mca_repeated_results.csv

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+large_overlap,85,1000,300,9.598291939181841,0.0891382967332148,True,9.2906505983555,0.08815586751086471,-0.30764134082634165,-0.0009824292223500897,3.9502490887884936e-05,54.77466388677481,54.774624384283925,0.03716903406151076,7171.973527402852,7171.93635836879,True,True,88729145.26798826,True,False,0.924,0.9999881676909779,0.9999999883297201
+large_overlap,86,1000,303,9.598291939181841,0.0891382967332148,True,9.77262717184347,0.09336132827009778,0.17433523266162787,0.004223031536882985,0.0658217905595087,15.776412882447673,15.710591091888164,0.043101243425939996,47.5715865439897,47.528485300563766,True,True,319046.07351818396,False,True,0.994,0.5681864808420696,0.9999683335660097
+large_overlap,87,1000,300,9.598291939181841,0.0891382967332148,True,9.512500686110421,0.13059373086543197,-0.08579125307142021,0.04145543413221717,6.680816074870277,10.540495202613073,3.8596791277427958,0.11368337798509295,0.2288685236405867,0.11518514565549376,True,False,4904391331.636687,True,False,0.999,0.1484023317983487,0.5699794474770237
+large_overlap,88,1000,283,9.598291939181841,0.0891382967332148,True,9.710333824966185,0.08064127758555363,0.11204188578434326,-0.00849701914766117,0.04682407255276806,12.745972648595686,12.699148576042917,0.05813594366111738,19.601783540621874,19.543647596960756,True,True,137247506.85893598,True,False,0.986,0.43581205807377743,0.9617318123804461
+large_overlap,89,1000,292,9.598291939181841,0.0891382967332148,True,9.519400166190808,0.10390776301125026,-0.07889177299103345,0.014769466278035465,0.16864592467356906,33.083707408748786,32.91506148407522,0.05616098527160498,21.03657381328745,20.980412828015844,True,True,inf,True,False,0.695,0.9842907019356175,0.9999864540765729
+large_overlap,90,1000,292,9.598291939181841,0.0891382967332148,True,9.83227198760838,0.0674738413817803,0.2339800484265382,-0.021664455351434506,0.022309539957407715,19.401317436220594,19.379007896263186,0.039973784128338755,60.97832273910971,60.93834895498137,True,True,65043.101498640506,False,True,1.0,0.6998311643303878,0.9993253999599384
+large_overlap,91,1000,289,9.598291939181841,0.0891382967332148,True,9.49414765310278,0.09624189468008894,-0.10414428607906068,0.007103597946874138,0.013391550705649648,16.084237390182,16.070845839476352,0.05505405224898055,124.11570689406703,124.06065284181805,True,True,61702.64173040521,False,True,0.998,0.5085334224937168,0.9989737954544056
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+large_overlap,93,1000,297,9.598291939181841,0.0891382967332148,True,9.868365562106943,0.10395228184397579,0.27007362292510173,0.014813985110760985,2.7901077366309903,11.388065254477558,8.597957517846568,0.08227770612563227,3.503894189706089,3.421616483580457,True,True,3629630262.1886244,True,False,0.997,0.2896636515124253,0.9955216088202098
+large_overlap,94,1000,278,9.598291939181841,0.0891382967332148,True,10.153691654898862,0.11356641485869588,0.5553997157170212,0.024428118125481083,0.0027714866918813743,43.45983413074937,43.45706264405749,0.0752260804415362,1829.4288575123603,1829.3536314319188,True,True,4816392.381342991,True,False,0.903,0.999959615585899,0.999999995370226
+large_overlap,95,1000,301,9.598291939181841,0.0891382967332148,True,9.730350003618538,0.09607058024845073,0.13205806443669665,0.006932283515235935,0.34344846798615236,11.259208662954546,10.915760194968394,0.07615244188890027,7.257373255466698,7.181220813577798,True,True,54142271.93405045,True,False,1.0,0.422434527452498,0.9999085710851429
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organized_uncertainty_analysis/examples/bayesian_synthetic/bayesian_mca_repeated_simulation.py

@@ -0,0 +1,160 @@
+"""Repeated simulation diagnostic for the constrained-Bayesian MCA procedure."""
+
+from __future__ import annotations
+
+import os
+import sys
+from concurrent.futures import ProcessPoolExecutor, as_completed
+from pathlib import Path
+
+import numpy as np
+import pandas as pd
+from scipy import stats
+
+SOURCE_ROOT = Path(r"C:\Users\zahra\Desktop\PHD FMF\PhD Thesis\OPTIMIZATION\uncertainty_study\python\Zahra\FINAL FILES")
+sys.path.insert(0, str(SOURCE_ROOT))
+
+from organized_uncertainty_analysis.bayesian.core import (  # noqa: E402
+    estimate_ci_bundle,
+    slope_at_x,
+    theta_max,
+    x_at_p,
+)
+
+ROOT = Path(__file__).resolve().parent
+DETAIL_FILE = ROOT / "bayesian_mca_repeated_results.csv"
+SUMMARY_FILE = ROOT / "bayesian_mca_repeated_summary.csv"
+
+REPLICATES = int(os.getenv("BAYES_MCA_REPLICATES", "100"))
+MCA_DRAWS = int(os.getenv("BAYES_MCA_DRAWS", "1000"))
+WORKERS = int(os.getenv("BAYES_MCA_WORKERS", "3"))
+
+# omega, a, b, scale, k, vartheta
+SCENARIOS = {
+    "large_clear": (1000, False, (0.30, 20.0, 8.0, 6.0, 16.0, 0.25)),
+    "large_overlap": (1000, False, (0.30, 8.0, 5.0, 4.0, 5.0, 1.0)),
+    "clinical_5AE": (58, True, (5.0 / 58.0, 8.0, 5.0, 4.0, 5.0, 1.0)),
+}
+
+
+def finite_interval(values):
+    z = np.asarray(values, float)
+    z = z[np.isfinite(z)]
+    if z.size < 2:
+        return np.nan, np.nan
+    return tuple(float(v) for v in np.quantile(z, [0.025, 0.975]))
+
+
+def generate_data(n, exact_five, pars, seed):
+    omega, a, b, scale, k, vartheta = pars
+    rng = np.random.default_rng(seed)
+    if exact_five:
+        y = np.zeros(n, dtype=int)
+        y[rng.choice(n, 5, replace=False)] = 1
+    else:
+        y = rng.binomial(1, omega, n).astype(int)
+    x = np.empty(n, dtype=float)
+    nc = y == 0
+    x[nc] = rng.gamma(k, vartheta, int(nc.sum()))
+    x[~nc] = stats.betaprime.rvs(a, b, scale=scale, size=int((~nc).sum()), random_state=rng)
+    return np.clip(x, 1e-10, None), y
+
+
+def run_one(task):
+    scenario_index, name, n, exact_five, pars, replicate = task
+    seed = 940000 + 10000 * scenario_index + replicate
+    omega, a, b, scale, k, vartheta = pars
+    cap = theta_max(a, b, k, scale)
+    true_theta = (*pars, cap)
+    true_x50 = x_at_p(true_theta, hi=50.0, hi_max=500.0)
+    true_s50 = slope_at_x(true_theta, true_x50)
+    x, y = generate_data(n, exact_five, pars, seed)
+    grid = np.linspace(max(1e-5, float(x.min() * 0.75)),
+                       max(15.0, float(np.quantile(x, 0.995) * 1.1)), 200)
+    base = {
+        "scenario": name, "replicate": replicate + 1, "n": n,
+        "events": int(y.sum()), "true_x50": true_x50, "true_s50": true_s50,
+    }
+    try:
+        fit = estimate_ci_bundle(
+            x, y, name, grid, B_nonpar=0, B_param=0, M_mca=MCA_DRAWS,
+            mca_seed=seed + 500000, seed=seed, use_prior_p=True,
+            prior_r=(1.05, 1.05), tau=25.0, n_starts_clean=3,
+            n_starts_boot=1, progress_every=MCA_DRAWS,
+            max_hessian_condition=1e6,
+        )
+        xlo, xhi = finite_interval(fit["x50_mca"])
+        slo, shi = finite_interval(fit["s50_mca"])
+        h = fit["hessian_diagnostics"]
+        m = fit["diagnostics_mca"]
+        width = np.asarray(fit["mca_hi"]) - np.asarray(fit["mca_lo"])
+        base.update(
+            fit_success=True, x50_hat=float(fit["x50"]), s50_hat=float(fit["s50"]),
+            x50_bias=float(fit["x50"] - true_x50), s50_bias=float(fit["s50"] - true_s50),
+            x50_lo=xlo, x50_hi=xhi, x50_width=xhi - xlo,
+            s50_lo=slo, s50_hi=shi, s50_width=shi - slo,
+            x50_covered=bool(xlo <= true_x50 <= xhi),
+            s50_covered=bool(slo <= true_s50 <= shi),
+            hessian_condition=float(h["original_condition_number"]),
+            hessian_stabilized=bool(h["stabilized"]),
+            hessian_reliable=bool(h["reliable"]),
+            mca_acceptance=float(m["successful_curve"] / max(m["attempted"], 1)),
+            band_mean_width=float(np.mean(width)), band_max_width=float(np.max(width)),
+        )
+    except Exception as exc:
+        base.update(fit_success=False, error=f"{type(exc).__name__}: {exc}")
+    return base
+
+
+def summarize(df):
+    rows = []
+    for name, block in df.groupby("scenario", sort=False):
+        ok = block[block["fit_success"] == True]  # noqa: E712
+        rows.append({
+            "scenario": name,
+            "replicates": len(block),
+            "fit_success_rate": len(ok) / len(block),
+            "median_events": block["events"].median(),
+            "x50_mean_bias": ok["x50_bias"].mean(),
+            "x50_coverage": ok["x50_covered"].mean(),
+            "x50_median_width": ok["x50_width"].median(),
+            "s50_mean_bias": ok["s50_bias"].mean(),
+            "s50_coverage": ok["s50_covered"].mean(),
+            "s50_median_width": ok["s50_width"].median(),
+            "median_mca_acceptance": ok["mca_acceptance"].median(),
+            "median_band_mean_width": ok["band_mean_width"].median(),
+            "median_band_max_width": ok["band_max_width"].median(),
+            "hessian_stabilization_rate": ok["hessian_stabilized"].mean(),
+            "hessian_reliable_rate": ok["hessian_reliable"].mean(),
+            "median_hessian_condition": ok["hessian_condition"].replace(np.inf, np.nan).median(),
+            "infinite_hessian_fraction": np.isinf(ok["hessian_condition"]).mean(),
+        })
+    return pd.DataFrame(rows)
+
+
+def main():
+    tasks = []
+    for scenario_index, (name, (n, exact_five, pars)) in enumerate(SCENARIOS.items()):
+        for replicate in range(REPLICATES):
+            tasks.append((scenario_index, name, n, exact_five, pars, replicate))
+
+    rows = []
+    with ProcessPoolExecutor(max_workers=WORKERS) as pool:
+        futures = [pool.submit(run_one, task) for task in tasks]
+        for completed, future in enumerate(as_completed(futures), 1):
+            rows.append(future.result())
+            if completed % 10 == 0 or completed == len(tasks):
+                pd.DataFrame(rows).sort_values(["scenario", "replicate"]).to_csv(DETAIL_FILE, index=False)
+                print(f"Completed {completed}/{len(tasks)}", flush=True)
+
+    detail = pd.DataFrame(rows).sort_values(["scenario", "replicate"])
+    detail.to_csv(DETAIL_FILE, index=False)
+    summary = summarize(detail)
+    summary.to_csv(SUMMARY_FILE, index=False)
+    print(summary.to_string(index=False), flush=True)
+    print(f"Details: {DETAIL_FILE}", flush=True)
+    print(f"Summary: {SUMMARY_FILE}", flush=True)
+
+
+if __name__ == "__main__":
+    main()

organized_uncertainty_analysis/examples/bayesian_synthetic/bayesian_mca_repeated_summary.csv

@@ -0,0 +1,4 @@
+scenario,replicates,fit_success_rate,median_events,x50_mean_bias,x50_coverage,x50_median_width,s50_mean_bias,s50_coverage,s50_median_width,median_mca_acceptance,median_band_mean_width,median_band_max_width,hessian_stabilization_rate,hessian_reliable_rate,median_hessian_condition,infinite_hessian_fraction
+clinical_5AE,100,1.0,5.0,3.514208552020449,0.99,41.002717698300515,0.05260331315583545,0.87,113.04474744531724,0.81,0.9986004598121373,1.0,0.96,0.04,120852170.14156757,0.14
+large_clear,100,1.0,297.5,0.012317117066697927,0.97,5.798565868980765,0.08486347561411217,0.88,2.1537270618995983,0.9995,0.11767405380674556,0.9999754919381231,1.0,0.0,2137701350.89387,0.68
+large_overlap,100,1.0,298.0,0.07764277632434181,1.0,12.754849841804202,0.004879896357503172,0.97,5.882924803747011,0.999,0.4480860864073774,0.9966624899817664,0.84,0.16,147211886.82937956,0.08

organized_uncertainty_analysis/examples/bayesian_synthetic/mca_diagnostic.py

@@ -0,0 +1,185 @@
+"""Controlled numerical diagnostic for constrained-Bayesian MCA.
+
+Data are generated exactly from the Gamma/Betaprime class-conditional model.
+This checks numerical behavior under the model assumptions; it is not a
+clinical validation or a simulation study of statistical performance.
+"""
+
+from __future__ import annotations
+
+import os
+import sys
+from pathlib import Path
+
+import matplotlib
+
+matplotlib.use("Agg")
+
+import matplotlib.pyplot as plt
+import numpy as np
+import pandas as pd
+from scipy import stats
+
+
+EXAMPLE_DIR = Path(__file__).resolve().parent
+PROJECT_ROOT = EXAMPLE_DIR.parents[1]
+if str(PROJECT_ROOT.parent) not in sys.path:
+    sys.path.insert(0, str(PROJECT_ROOT.parent))
+
+from organized_uncertainty_analysis.bayesian.core import (
+    P_with,
+    estimate_ci_bundle,
+    slope_at_x,
+    theta_max,
+    x_at_p,
+)
+
+
+SEED = 20260914
+SAMPLE_SIZES = (1000, 500, 200, 60)
+MCA_DRAWS = int(os.getenv("BAYES_MCA_DIAGNOSTIC_DRAWS", "5000"))
+OUTPUT_DIR = Path(
+    os.getenv("BAYES_MCA_DIAGNOSTIC_OUTPUT", str(EXAMPLE_DIR / "mca_diagnostic_outputs"))
+).resolve()
+OUTPUT_DIR.mkdir(parents=True, exist_ok=True)
+
+# Feasible generating parameters: omega, a, b, s, k, vartheta.
+OMEGA = 0.30
+A = 8.0
+B = 5.0
+S = 4.0
+K = 5.0
+VARTTHETA = 1.0
+CAP = theta_max(A, B, K, S)
+if not (0.0 < VARTTHETA < CAP):
+    raise RuntimeError("The selected generating parameters violate the model constraints.")
+TRUE_THETA = (OMEGA, A, B, S, K, VARTTHETA, CAP)
+
+
+def generate_exact_model_data(n: int, seed: int) -> tuple[np.ndarray, np.ndarray]:
+    """Draw y from prevalence and x from the matching class distribution."""
+    rng = np.random.default_rng(seed)
+    y = rng.binomial(1, OMEGA, size=n).astype(int)
+    x = np.empty(n, dtype=float)
+    nc = y == 0
+    ae = ~nc
+    x[nc] = rng.gamma(shape=K, scale=VARTTHETA, size=int(nc.sum()))
+    x[ae] = stats.betaprime.rvs(A, B, scale=S, size=int(ae.sum()), random_state=rng)
+    return np.clip(x, 1e-12, None), y
+
+
+def interval(values: np.ndarray) -> tuple[float, float]:
+    values = np.asarray(values, float)
+    values = values[np.isfinite(values)]
+    if not len(values):
+        return np.nan, np.nan
+    lo, hi = np.quantile(values, [0.025, 0.975])
+    return float(lo), float(hi)
+
+
+def run_one(n: int, seed: int):
+    x, y = generate_exact_model_data(n, seed)
+    x_upper = max(float(np.quantile(x, 0.995) * 1.10), 12.0)
+    x_grid = np.linspace(max(1e-5, float(x.min()) * 0.75), x_upper, 400)
+    result = estimate_ci_bundle(
+        x,
+        y,
+        f"n={n}",
+        x_grid,
+        B_nonpar=0,
+        B_param=0,
+        M_mca=MCA_DRAWS,
+        mca_seed=seed + 10000,
+        seed=seed,
+        use_prior_p=True,
+        prior_r=(1.05, 1.05),
+        tau=25.0,
+        n_starts_clean=5,
+        n_starts_boot=1,
+        progress_every=max(MCA_DRAWS, 1),
+        max_hessian_condition=1e6,
+    )
+
+    h = result["hessian_diagnostics"]
+    m = result["diagnostics_mca"]
+    x50_lo, x50_hi = interval(result["x50_mca"])
+    s50_lo, s50_hi = interval(result["s50_mca"])
+    band_width = np.asarray(result["mca_hi"]) - np.asarray(result["mca_lo"])
+
+    summary = {
+        "n": n,
+        "events": int(y.sum()),
+        "event_fraction": float(y.mean()),
+        "objective": float(result["objective"]),
+        "x50_hat": float(result["x50"]),
+        "x50_mca_lo": x50_lo,
+        "x50_mca_hi": x50_hi,
+        "s50_hat": float(result["s50"]),
+        "s50_mca_lo": s50_lo,
+        "s50_mca_hi": s50_hi,
+        "hessian_min_eigenvalue": float(h["minimum_eigenvalue"]),
+        "hessian_original_condition": float(h["original_condition_number"]),
+        "hessian_positive_definite": bool(h["original_positive_definite"]),
+        "hessian_stabilized": bool(h["stabilized"]),
+        "hessian_reliable": bool(h["reliable"]),
+        "mca_attempted": int(m["attempted"]),
+        "mca_accepted": int(m["successful_curve"]),
+        "mca_acceptance_fraction": float(m["successful_curve"] / max(m["attempted"], 1)),
+        "mca_band_mean_width": float(np.mean(band_width)),
+        "mca_band_max_width": float(np.max(band_width)),
+    }
+
+    curve_table = pd.DataFrame(
+        {
+            "n": n,
+            "x": x_grid,
+            "true_probability": P_with(TRUE_THETA, x_grid),
+            "fitted_probability": result["pmap"],
+            "mca_lower": result["mca_lo"],
+            "mca_upper": result["mca_hi"],
+        }
+    )
+    return summary, curve_table
+
+
+def main() -> None:
+    true_x50 = x_at_p(TRUE_THETA, hi=20.0, hi_max=200.0)
+    true_s50 = slope_at_x(TRUE_THETA, true_x50)
+    summaries = []
+    curves = []
+    for index, n in enumerate(SAMPLE_SIZES):
+        summary, curve = run_one(n, SEED + index)
+        summaries.append(summary)
+        curves.append(curve)
+
+    summary_table = pd.DataFrame(summaries)
+    summary_table.insert(3, "true_x50", true_x50)
+    summary_table.insert(7, "true_s50", true_s50)
+    curve_table = pd.concat(curves, ignore_index=True)
+    summary_table.to_csv(OUTPUT_DIR / "mca_diagnostic_summary.csv", index=False)
+    curve_table.to_csv(OUTPUT_DIR / "mca_diagnostic_curves.csv", index=False)
+
+    fig, axes = plt.subplots(2, 2, figsize=(12, 8), sharey=True)
+    for ax, n in zip(axes.flat, SAMPLE_SIZES):
+        block = curve_table[curve_table["n"] == n]
+        ax.fill_between(block["x"], block["mca_lower"], block["mca_upper"], alpha=0.22)
+        ax.plot(block["x"], block["true_probability"], "--", color="tab:orange", label="generating risk")
+        ax.plot(block["x"], block["fitted_probability"], color="black", label="MAP fit")
+        ax.set_title(f"n={n}")
+        ax.set_xlabel("x")
+        ax.set_ylim(-0.02, 1.02)
+    axes[0, 0].set_ylabel("P(y=1 | x)")
+    axes[1, 0].set_ylabel("P(y=1 | x)")
+    axes[0, 0].legend(frameon=True)
+    fig.tight_layout()
+    fig.savefig(OUTPUT_DIR / "mca_diagnostic.png", dpi=300, bbox_inches="tight")
+    fig.savefig(OUTPUT_DIR / "mca_diagnostic.pdf", bbox_inches="tight")
+    plt.close(fig)
+
+    print(f"True x50={true_x50:.6f}; true s50={true_s50:.6f}")
+    print(summary_table.to_string(index=False))
+    print(f"\nOutputs: {OUTPUT_DIR}")
+
+
+if __name__ == "__main__":
+    main()

organized_uncertainty_analysis/examples/bayesian_synthetic/mca_diagnostic_outputs/mca_diagnostic_curves.csv

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organized_uncertainty_analysis/examples/bayesian_synthetic/mca_diagnostic_outputs/mca_diagnostic_summary.csv

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organized_uncertainty_analysis/examples/bayesian_synthetic/outputs_notebook/synthetic_bayesian_elasticity.csv

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organized_uncertainty_analysis/examples/bayesian_synthetic/outputs_notebook/synthetic_bayesian_fit_gof.csv

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organized_uncertainty_analysis/examples/bayesian_synthetic/outputs_notebook/synthetic_bayesian_noise_summary.csv

@@ -0,0 +1,5 @@
+Dataset,NoiseType,Sigma,x50,Delta_refit_at_x50,Delta_tta_at_x50,N_refit_success,N_tta
+FULL,multiplicative,0.1,10.44529210771819,0.08019639260161027,0.3048460029970775,20,500
+FULL,additive,0.5381659276708483,10.44529210771819,0.03726850741180965,0.13826354352136805,20,500
+TRIM,multiplicative,0.1,10.503457299688199,0.10583683518816772,0.30083357635961705,20,500
+TRIM,additive,0.5381659276708483,10.503457299688199,0.048630170166524656,0.14019721823420334,20,500

organized_uncertainty_analysis/examples/bayesian_synthetic/outputs_notebook/synthetic_bayesian_parameter_ci.csv

@@ -0,0 +1,13 @@
+Dataset,Parameter,Estimate,Wald_LL,Wald_UL,NPBS_LL,NPBS_UL,PBS_LL,PBS_UL,MCA_LL,MCA_UL
+FULL,omega,0.5090710040607127,0.3047663527301474,0.713375655391278,0.5087297653600056,0.5093992668078418,0.5086937512662236,0.5104833758355859,0.32266825753570155,0.7140682478588226
+FULL,a,30.418113183821067,-41.963970515752834,102.80019688339496,25.115538602311524,382.79854527066846,1.8351521508561361,376.5658715436641,8.88645268434805,146.945502644559
+FULL,b,22.466107924668375,-309.6403994727741,354.5726153221109,1.9334455070490169,855.2120598157326,0.6069907505383557,496.9218728402604,1e-06,364.40642662928286
+FULL,s,7.872718890586231,-93.43765649511597,109.18309427628843,0.14142149864945194,59.845678695826464,0.3264956448557201,637.8047223331417,1e-06,112.87780891980279
+FULL,k,18.786273835285517,-106.0724098027695,143.64495747334053,7.298127648957493,145.21056674910088,0.3212021468621087,131.80237913825198,1e-06,146.94550164455902
+FULL,vartheta,0.4905127909939689,-2.282349944179935,3.2633755261678727,0.09255208265827314,1.0227200664106155,0.08225645888123984,27.615911937932513,2.9703948287031138e-05,34231800.97394332
+TRIM,omega,0.5137326574224635,0.3094852319995566,0.7179800828453705,0.513472805304309,0.5148746663627274,0.5135449776899557,0.5238337483607554,0.3355405763617509,0.7005089956967289
+TRIM,a,63.41331795589869,-20.008553262325165,146.83518917412255,24.081824472221644,452.35434523285096,1.5322640227905584,1354.0475625301415,8.886127907912563,153.7276937142527
+TRIM,b,167.31111693993313,-225.1084889789684,559.7307228588347,5.0589845454031295,169.1691083702932,15.86172276013983,193.62070487487478,1e-06,565.9860130878385
+TRIM,s,28.295787116354,-18.428049799578687,75.01962403228669,0.19247854973822545,189.0883957025952,1.47526227750346,1195.9770349342646,1.0402315640918973e-06,76.7913378328144
+TRIM,k,54.20966857673099,-22.358337691501674,130.77767484496366,8.03152520647744,78.41350183361476,0.0922728621838004,220.41230712170852,3.6370806388489254,136.04168076545443
+TRIM,vartheta,0.18675297209877512,-0.04653984265190245,0.4200457868494527,0.14339020056784418,0.980996945355759,0.04896863091620394,75.55294726933506,3.605136472312827e-07,1.657110357674498

organized_uncertainty_analysis/examples/bayesian_synthetic/outputs_notebook/synthetic_bayesian_x50_s50_ci.csv

@@ -0,0 +1,5 @@
+Dataset,Characteristic,Estimate,Wald_LL,Wald_UL,NPBS_LL,NPBS_UL,PBS_LL,PBS_UL,MCA_LL,MCA_UL
+FULL,x50,10.445292107718178,7.9706821031482775,12.919902112288078,8.118222823211987,11.786223095255364,8.720578138924585,12.691679646129336,4.834323900192829e-05,39.56123698372326
+FULL,s50,0.06631811305935538,0.0017053370508177262,0.13093088906789302,0.022296296808249287,0.12313752805407183,0.011186907836630032,0.12301291010710969,0.04940014273494866,4855.642956091497
+TRIM,x50,10.503457299688245,8.116925360354607,12.889989239021883,7.580237496929739,11.947507185326835,6.94228150492522,11.243319088822343,1.8723696809249075e-05,43.62311304656788
+TRIM,s50,0.07107369556624184,0.013295132310711472,0.1288522588217722,0.03830359813790108,0.12658756160897888,0.02143853854235933,0.18254867224619872,0.03693909638204792,8120.211746536521

organized_uncertainty_analysis/examples/bayesian_synthetic/outputs_smoke/synthetic_bayesian_elasticity.csv

@@ -0,0 +1,13 @@
+Dataset,Parameter,Elasticity_x50,Elasticity_s50
+FULL,omega,-0.7351375022391612,-1.4760585776061559
+FULL,a,0.017821930973054827,4.753871085390238
+FULL,b,-0.19907028976488453,-5.0230631154300465
+FULL,s,0.09473063862823096,4.867580158763073
+FULL,k,1.0317764297887233,-4.708301402651632
+FULL,vartheta,0.9052693429672183,-5.86758042177526
+TRIM,omega,-0.6886899409015484,-1.7770560655902257
+TRIM,a,0.1998177317688946,16.002972447469457
+TRIM,b,-0.3644183131484693,-16.10847472668061
+TRIM,s,0.31922402477960415,16.078275842657213
+TRIM,k,0.8362807504048542,-15.996243930978547
+TRIM,vartheta,0.6807759505308644,-17.078276434479324

organized_uncertainty_analysis/examples/bayesian_synthetic/outputs_smoke/synthetic_bayesian_fit_gof.csv

@@ -0,0 +1,3 @@
+Dataset,omega,a,b,s,k,vartheta,n,events,log_loss,brier_score,accuracy,sensitivity,specificity
+FULL,0.5090710040607127,30.418113183821067,22.466107924668375,7.872718890586231,18.786273835285517,0.4905127909939689,120,61,0.4642729423045881,0.15664415547251226,0.75,0.7049180327868853,0.7966101694915254
+TRIM,0.5137326574224635,63.41331795589869,167.31111693993313,28.295787116354,54.20966857673099,0.18675297209877512,119,61,0.447164606910317,0.15153215569855594,0.7647058823529411,0.7049180327868853,0.8275862068965517

organized_uncertainty_analysis/examples/bayesian_synthetic/outputs_smoke/synthetic_bayesian_noise_summary.csv

@@ -0,0 +1,5 @@
+Dataset,NoiseType,Sigma,x50,Delta_refit_at_x50,Delta_tta_at_x50,N_refit_success,N_tta
+FULL,multiplicative,0.1,10.44529210771819,0.07116717384279508,0.2335242115660422,5,50
+FULL,additive,0.5381659276708483,10.44529210771819,0.027436240861708705,0.14208244601980485,5,50
+TRIM,multiplicative,0.1,10.503457299688199,0.0817746815779003,0.31251359624510705,5,50
+TRIM,additive,0.5381659276708483,10.503457299688199,0.04713683334679858,0.15671133012987282,5,50

organized_uncertainty_analysis/examples/bayesian_synthetic/outputs_smoke/synthetic_bayesian_parameter_ci.csv

@@ -0,0 +1,13 @@
+Dataset,Parameter,Estimate,Wald_LL,Wald_UL,NPBS_LL,NPBS_UL,PBS_LL,PBS_UL,MCA_LL,MCA_UL
+FULL,omega,0.5090710040607127,0.3047663527301474,0.713375655391278,0.508831504799427,0.5094190631915105,0.5088688474942864,0.5091358096994106,0.3321392880591583,0.7079678656222822
+FULL,a,30.418113183821067,-41.963970515752834,102.80019688339496,23.955682118581656,400.73898108341234,7.267377223819878,289.86411203493475,9.206303971908097,143.3828545973056
+FULL,b,22.466107924668375,-309.6403994727741,354.5726153221109,2.3857306571177777,180.264858794948,2.0699090323285394,307.73759149570515,1e-06,345.08011990745166
+FULL,s,7.872718890586231,-93.43765649511597,109.18309427628843,0.18593321950005534,46.490135069331245,0.2531086870733385,41.07741230528736,1e-06,111.05172170201483
+FULL,k,18.786273835285517,-106.0724098027695,143.64495747334053,6.781343567006571,35.33024592565538,5.439436392198149,82.27918868533428,1e-06,143.3828535973056
+FULL,vartheta,0.4905127909939689,-2.282349944179935,3.2633755261678727,0.28044887628224613,1.0752515551842294,0.11767729413712272,1.437159043290308,4.495536464380542e-05,25575754.197645478
+TRIM,omega,0.5137326574224635,0.3094852319995566,0.7179800828453705,0.5134678789494422,0.5151205498516945,0.5135774138598597,0.5201280873419334,0.33358955896685727,0.7022534250589182
+TRIM,a,63.41331795589869,-20.008553262325165,146.83518917412255,14.39668434259248,361.46062356272006,4.777950436485138,1550.6452048937572,5.727303885424245,147.00634452176308
+TRIM,b,167.31111693993313,-225.1084889789684,559.7307228588347,6.440156990580704,169.19633119418762,120.9008061750779,170.84944481603358,1e-06,526.9669335628475
+TRIM,s,28.295787116354,-18.428049799578687,75.01962403228669,0.19262954135537608,260.5342839795767,1.1506536452527594,379.21716799306364,1.0052558108144761e-06,68.10102751849456
+TRIM,k,54.20966857673099,-22.358337691501674,130.77767484496366,6.671143244855734,66.16369909230758,4.777923378348499,170.6886818959853,1.0791406835121566,132.13472855507277
+TRIM,vartheta,0.18675297209877512,-0.04653984265190245,0.4200457868494527,0.15429644002538817,1.10001215479923,0.06466065071827731,1.4915533782426675,1.066310337289433e-06,1.2531091974548252

organized_uncertainty_analysis/examples/bayesian_synthetic/outputs_smoke/synthetic_bayesian_x50_s50_ci.csv

@@ -0,0 +1,5 @@
+Dataset,Characteristic,Estimate,Wald_LL,Wald_UL,NPBS_LL,NPBS_UL,PBS_LL,PBS_UL,MCA_LL,MCA_UL
+FULL,x50,10.445292107718178,7.9706821031482775,12.919902112288078,8.534284379735277,11.67447105511564,9.594853087767333,11.526619036727611,4.7728696075267204e-05,36.77639994674275
+FULL,s50,0.06631811305935538,0.0017053370508177262,0.13093088906789302,0.04401895940159717,0.10111925165152161,0.026842528826021558,0.12613374203769212,0.049863695548360364,4744.200615384892
+TRIM,x50,10.503457299688245,8.116925360354607,12.889989239021883,7.458477557385079,11.435376676370986,9.442840406969182,11.637648492203425,2.8418267874286857e-05,36.716081618883
+TRIM,s50,0.07107369556624184,0.013295132310711472,0.1288522588217722,0.03280549644560361,0.11492609827844871,0.03612112013929354,0.1110676296842183,0.036845325774415565,7377.535824210336

organized_uncertainty_analysis/examples/bayesian_synthetic/outputs_smoke_v2/synthetic_bayesian_elasticity.csv

@@ -0,0 +1,13 @@
+Dataset,Parameter,Elasticity_x50,Elasticity_s50
+FULL,omega,-0.7351375022391612,-1.4760585776061559
+FULL,a,0.017821930973054827,4.753871085390238
+FULL,b,-0.19907028976488453,-5.0230631154300465
+FULL,s,0.09473063862823096,4.867580158763073
+FULL,k,1.0317764297887233,-4.708301402651632
+FULL,vartheta,0.9052693429672183,-5.86758042177526
+TRIM,omega,-0.6886899409015484,-1.7770560655902257
+TRIM,a,0.1998177317688946,16.002972447469457
+TRIM,b,-0.3644183131484693,-16.10847472668061
+TRIM,s,0.31922402477960415,16.078275842657213
+TRIM,k,0.8362807504048542,-15.996243930978547
+TRIM,vartheta,0.6807759505308644,-17.078276434479324

organized_uncertainty_analysis/examples/bayesian_synthetic/outputs_smoke_v2/synthetic_bayesian_fit_gof.csv

@@ -0,0 +1,3 @@
+Dataset,omega,a,b,s,k,vartheta,n,events,log_loss,brier_score,accuracy,sensitivity,specificity
+FULL,0.5090710040607127,30.418113183821067,22.466107924668375,7.872718890586231,18.786273835285517,0.4905127909939689,120,61,0.4642729423045881,0.15664415547251226,0.75,0.7049180327868853,0.7966101694915254
+TRIM,0.5137326574224635,63.41331795589869,167.31111693993313,28.295787116354,54.20966857673099,0.18675297209877512,119,61,0.447164606910317,0.15153215569855594,0.7647058823529411,0.7049180327868853,0.8275862068965517

organized_uncertainty_analysis/examples/bayesian_synthetic/outputs_smoke_v2/synthetic_bayesian_noise_summary.csv

@@ -0,0 +1,5 @@
+Dataset,NoiseType,Sigma,x50,Delta_refit_at_x50,Delta_tta_at_x50,N_refit_success,N_tta
+FULL,multiplicative,0.1,10.44529210771819,0.07116717384279508,0.2335242115660422,5,50
+FULL,additive,0.5381659276708483,10.44529210771819,0.027436240861708705,0.14208244601980485,5,50
+TRIM,multiplicative,0.1,10.503457299688199,0.0817746815779003,0.31251359624510705,5,50
+TRIM,additive,0.5381659276708483,10.503457299688199,0.04713683334679858,0.15671133012987282,5,50

organized_uncertainty_analysis/examples/bayesian_synthetic/outputs_smoke_v2/synthetic_bayesian_parameter_ci.csv

@@ -0,0 +1,13 @@
+Dataset,Parameter,Estimate,Wald_LL,Wald_UL,NPBS_LL,NPBS_UL,PBS_LL,PBS_UL,MCA_LL,MCA_UL
+FULL,omega,0.5090710040607127,0.3047663527301474,0.713375655391278,0.508831504799427,0.5094190631915105,0.5088688474942864,0.5091358096994106,0.3321392880591583,0.7079678656222822
+FULL,a,30.418113183821067,-41.963970515752834,102.80019688339496,23.955682118581656,400.73898108341234,7.267377223819878,289.86411203493475,9.206303971908097,143.3828545973056
+FULL,b,22.466107924668375,-309.6403994727741,354.5726153221109,2.3857306571177777,180.264858794948,2.0699090323285394,307.73759149570515,1e-06,345.08011990745166
+FULL,s,7.872718890586231,-93.43765649511597,109.18309427628843,0.18593321950005534,46.490135069331245,0.2531086870733385,41.07741230528736,1e-06,111.05172170201483
+FULL,k,18.786273835285517,-106.0724098027695,143.64495747334053,6.781343567006571,35.33024592565538,5.439436392198149,82.27918868533428,1e-06,143.3828535973056
+FULL,vartheta,0.4905127909939689,-2.282349944179935,3.2633755261678727,0.28044887628224613,1.0752515551842294,0.11767729413712272,1.437159043290308,4.495536464380542e-05,25575754.197645478
+TRIM,omega,0.5137326574224635,0.3094852319995566,0.7179800828453705,0.5134678789494422,0.5151205498516945,0.5135774138598597,0.5201280873419334,0.33358955896685727,0.7022534250589182
+TRIM,a,63.41331795589869,-20.008553262325165,146.83518917412255,14.39668434259248,361.46062356272006,4.777950436485138,1550.6452048937572,5.727303885424245,147.00634452176308
+TRIM,b,167.31111693993313,-225.1084889789684,559.7307228588347,6.440156990580704,169.19633119418762,120.9008061750779,170.84944481603358,1e-06,526.9669335628475
+TRIM,s,28.295787116354,-18.428049799578687,75.01962403228669,0.19262954135537608,260.5342839795767,1.1506536452527594,379.21716799306364,1.0052558108144761e-06,68.10102751849456
+TRIM,k,54.20966857673099,-22.358337691501674,130.77767484496366,6.671143244855734,66.16369909230758,4.777923378348499,170.6886818959853,1.0791406835121566,132.13472855507277
+TRIM,vartheta,0.18675297209877512,-0.04653984265190245,0.4200457868494527,0.15429644002538817,1.10001215479923,0.06466065071827731,1.4915533782426675,1.066310337289433e-06,1.2531091974548252

organized_uncertainty_analysis/examples/bayesian_synthetic/outputs_smoke_v2/synthetic_bayesian_x50_s50_ci.csv

@@ -0,0 +1,5 @@
+Dataset,Characteristic,Estimate,Wald_LL,Wald_UL,NPBS_LL,NPBS_UL,PBS_LL,PBS_UL,MCA_LL,MCA_UL
+FULL,x50,10.445292107718178,7.9706821031482775,12.919902112288078,8.534284379735277,11.67447105511564,9.594853087767333,11.526619036727611,4.7728696075267204e-05,36.77639994674275
+FULL,s50,0.06631811305935538,0.0017053370508177262,0.13093088906789302,0.04401895940159717,0.10111925165152161,0.026842528826021558,0.12613374203769212,0.049863695548360364,4744.200615384892
+TRIM,x50,10.503457299688245,8.116925360354607,12.889989239021883,7.458477557385079,11.435376676370986,9.442840406969182,11.637648492203425,2.8418267874286857e-05,36.716081618883
+TRIM,s50,0.07107369556624184,0.013295132310711472,0.1288522588217722,0.03280549644560361,0.11492609827844871,0.03612112013929354,0.1110676296842183,0.036845325774415565,7377.535824210336

organized_uncertainty_analysis/examples/bayesian_synthetic/run_synthetic_bayesian.py

@@ -0,0 +1,198 @@
+"""Run the constrained Bayesian workflow on generic synthetic x/y data.
+
+This is a software and reproducibility test, not a validation study.
+"""
+
+from __future__ import annotations
+
+import os
+import sys
+from pathlib import Path
+
+import matplotlib
+
+matplotlib.use("Agg")
+
+import matplotlib.pyplot as plt
+import numpy as np
+import pandas as pd
+
+
+EXAMPLE_DIR = Path(__file__).resolve().parent
+PROJECT_ROOT = EXAMPLE_DIR.parents[1]
+if str(PROJECT_ROOT.parent) not in sys.path:
+    sys.path.insert(0, str(PROJECT_ROOT.parent))
+
+from organized_uncertainty_analysis.bayesian import ci_estimation as ci
+from organized_uncertainty_analysis.bayesian import elasticity as el
+from organized_uncertainty_analysis.bayesian import noise_measurement as noise
+from organized_uncertainty_analysis.bayesian.data_fit_gof import fit_bayes, goodness_of_fit
+
+
+SEED = 20260913
+N = 120
+BOOTSTRAPS = int(os.getenv("SYNTHETIC_BAYES_BOOTSTRAPS", "100"))
+MCA_DRAWS = int(os.getenv("SYNTHETIC_BAYES_MCA_DRAWS", "5000"))
+NOISE_REFITS = int(os.getenv("SYNTHETIC_BAYES_NOISE_REFITS", "100"))
+NOISE_DRAWS = int(os.getenv("SYNTHETIC_BAYES_NOISE_DRAWS", "1000"))
+NOISE_MULT = float(os.getenv("SYNTHETIC_BAYES_NOISE_MULT", "0.10"))
+NOISE_ADD_SD_FRACTION = float(os.getenv("SYNTHETIC_BAYES_NOISE_ADD_SD_FRACTION", "0.10"))
+OUTPUT_DIR = Path(os.getenv("SYNTHETIC_BAYES_OUTPUT_DIR", str(EXAMPLE_DIR / "outputs"))).resolve()
+OUTPUT_DIR.mkdir(parents=True, exist_ok=True)
+
+
+def generate_data(seed: int = SEED, n: int = N) -> tuple[np.ndarray, np.ndarray]:
+    """Generate generic positive x and binary y with a fixed seed."""
+    rng = np.random.default_rng(seed)
+    x = rng.uniform(1.0, 20.0, size=n)
+    probability = 1.0 / (1.0 + np.exp(-(-4.0 + 0.4 * x)))
+    y = rng.binomial(1, probability).astype(int)
+    if np.unique(y).size != 2:
+        raise RuntimeError("Synthetic generation did not produce both classes.")
+    return x.astype(float), y
+
+
+def make_second_dataset(x: np.ndarray, y: np.ndarray) -> tuple[np.ndarray, np.ndarray]:
+    """Remove one high-valued y=0 observation to exercise the second data path."""
+    nc = np.flatnonzero(y == 0)
+    remove_index = nc[np.argmax(x[nc])]
+    keep = np.ones(len(y), dtype=bool)
+    keep[remove_index] = False
+    return x[keep], y[keep]
+
+
+def save_data(x: np.ndarray, y: np.ndarray) -> None:
+    pd.DataFrame({"x": x, "y": y}).to_csv(EXAMPLE_DIR / "synthetic_data.csv", index=False)
+
+
+def run_fit(data):
+    result = {"data": data}
+    rows = []
+    for index, dataset in enumerate(("FULL", "TRIM")):
+        x, y = data[dataset]
+        theta, optimizer = fit_bayes(x, y, seed=SEED + index, n_starts=3)
+        gof = goodness_of_fit(x, y, theta)
+        result[dataset] = {"theta": theta, "optimizer": optimizer, "gof": gof}
+        rows.append(
+            {
+                "Dataset": dataset,
+                "omega": theta[0],
+                "a": theta[1],
+                "b": theta[2],
+                "s": theta[3],
+                "k": theta[4],
+                "vartheta": theta[5],
+                **gof,
+            }
+        )
+    table = pd.DataFrame(rows)
+    table.to_csv(OUTPUT_DIR / "synthetic_bayesian_fit_gof.csv", index=False)
+    return result, table
+
+
+def run_ci(data):
+    x_full, y_full = data["FULL"]
+    x_trim, y_trim = data["TRIM"]
+    x_min = 0.75 * min(float(x_full.min()), float(x_trim.min()))
+    x_max = 1.05 * max(float(x_full.max()), float(x_trim.max()))
+    x_grid = np.linspace(max(1e-8, x_min), x_max, 300)
+    common = dict(
+        B_nonpar=BOOTSTRAPS,
+        B_param=BOOTSTRAPS,
+        M_mca=MCA_DRAWS,
+        use_prior_p=True,
+        prior_r=(1.05, 1.05),
+        tau=25.0,
+        n_starts_clean=2,
+        n_starts_boot=1,
+        progress_every=max(BOOTSTRAPS, 1),
+    )
+    full = ci.estimate_ci_bundle(
+        x_full, y_full, "FULL", x_grid, seed=SEED, mca_seed=SEED + 1000, **common
+    )
+    trim = ci.estimate_ci_bundle(
+        x_trim, y_trim, "TRIM", x_grid, seed=SEED + 1, mca_seed=SEED + 1001, **common
+    )
+    result = {
+        "X_orig": x_full,
+        "y_orig": y_full,
+        "X_trim": x_trim,
+        "y_trim": y_trim,
+        "x_grid": x_grid,
+        "orig": full,
+        "trim": trim,
+    }
+    parameter_table = ci.make_parameter_ci_table(result)
+    derived_table = ci.make_derived_ci_table(result)
+    parameter_table.to_csv(OUTPUT_DIR / "synthetic_bayesian_parameter_ci.csv", index=False)
+    derived_table.to_csv(OUTPUT_DIR / "synthetic_bayesian_x50_s50_ci.csv", index=False)
+    figure, _ = ci.plot_bayesian_ci(result, xmax=x_max, band_support="observed")
+    figure.savefig(OUTPUT_DIR / "synthetic_bayesian_ci_bands.png", dpi=300, bbox_inches="tight")
+    figure.savefig(OUTPUT_DIR / "synthetic_bayesian_ci_bands.pdf", bbox_inches="tight")
+    plt.close(figure)
+    return result, parameter_table, derived_table
+
+
+def run_elasticity(fit_result):
+    table = el.elasticity_full_trim(fit_result)
+    table.to_csv(OUTPUT_DIR / "synthetic_bayesian_elasticity.csv", index=False)
+    figure, _ = el.plot_combined_elasticity(table)
+    figure.savefig(OUTPUT_DIR / "synthetic_bayesian_elasticity.png", dpi=300, bbox_inches="tight")
+    figure.savefig(OUTPUT_DIR / "synthetic_bayesian_elasticity.pdf", bbox_inches="tight")
+    plt.close(figure)
+    return table
+
+
+def run_noise(data):
+    x_full, y_full = data["FULL"]
+    x_trim, y_trim = data["TRIM"]
+    x_max = 1.05 * max(float(x_full.max()), float(x_trim.max()))
+    sigma_add = NOISE_ADD_SD_FRACTION * float(np.std(x_full, ddof=1))
+    common = dict(
+        sigma_mult=NOISE_MULT,
+        sigma_add=sigma_add,
+        x_max=x_max,
+        grid_n=400,
+        n_refit=NOISE_REFITS,
+        n_tta=NOISE_DRAWS,
+        use_prior_p=True,
+        prior_r=(1.05, 1.05),
+        tau=25.0,
+    )
+    full = noise.build_bands_for_dataset(x_full, y_full, seed=SEED, **common)
+    trim = noise.build_bands_for_dataset(x_trim, y_trim, seed=SEED + 1, **common)
+    result = {"full": full, "trim": trim}
+    table = noise.make_noise_summary_table(result)
+    table.to_csv(OUTPUT_DIR / "synthetic_bayesian_noise_summary.csv", index=False)
+    figure, _ = noise.plot_4panels(
+        full,
+        trim,
+        save_prefix=OUTPUT_DIR / "synthetic_bayesian_noise",
+        x_max=x_max,
+        sigma_mult=NOISE_MULT,
+        sigma_add=sigma_add,
+    )
+    plt.close(figure)
+    return result, table
+
+
+def main():
+    x_full, y_full = generate_data()
+    x_trim, y_trim = make_second_dataset(x_full, y_full)
+    data = {"FULL": (x_full, y_full), "TRIM": (x_trim, y_trim)}
+    save_data(x_full, y_full)
+    print(f"Synthetic FULL: n={len(y_full)}, y=1={int(y_full.sum())}, y=0={int((1-y_full).sum())}")
+    print(f"Synthetic TRIM: n={len(y_trim)}, y=1={int(y_trim.sum())}, y=0={int((1-y_trim).sum())}")
+    fit_result, fit_table = run_fit(data)
+    _, parameter_table, derived_table = run_ci(data)
+    elasticity_table = run_elasticity(fit_result)
+    _, noise_table = run_noise(data)
+    print("\nFit and goodness of fit:\n", fit_table.to_string(index=False))
+    print("\nDerived intervals:\n", derived_table.to_string(index=False))
+    print("\nElasticity:\n", elasticity_table.to_string(index=False))
+    print("\nNoise summary:\n", noise_table.to_string(index=False))
+    print(f"\nSynthetic Bayesian workflow completed. Outputs: {OUTPUT_DIR}")
+
+
+if __name__ == "__main__":
+    main()

organized_uncertainty_analysis/examples/bayesian_synthetic/synthetic_data.csv

@@ -0,0 +1,121 @@
+x,y
+5.074400336813978,1
+7.712645142735211,0
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organized_uncertainty_analysis/examples/logistic_synthetic/README.md

@@ -0,0 +1,55 @@
+# Synthetic logistic reproducibility example
+
+This example runs the existing logistic analysis functions on reproducible,
+generic synthetic `x` and `y` data. The predictor is not on the SUV scale and
+does not represent a clinical biomarker. It is a software and reproducibility
+test, not a statistical or clinical validation of the models.
+
+Run from any directory with:
+
+```bash
+python examples/logistic_synthetic/run_synthetic_logistic.py
+```
+
+The same workflow is also available as four independent stages:
+
+```text
+synthetic_logistic_01.py  data, fitting, and goodness of fit
+synthetic_logistic_02.py  uncertainty intervals and confidence bands
+synthetic_logistic_03.py  elasticity of x50 and s50
+synthetic_logistic_04.py  additive and multiplicative measurement noise
+```
+
+`synthetic_logistic_notebook.ipynb` presents these stages in one clean notebook
+that can be restarted and run from top to bottom without hidden state.
+
+The script uses fixed random seeds and writes the generated data, tables, and
+figures to `examples/logistic_synthetic/outputs/`.
+
+Set `SYNTHETIC_OUTPUT_DIR` to write a run to a different folder, for example
+when an existing PDF is open and locked by a viewer on Windows.
+
+The measurement-noise magnitudes can be changed with `SYNTHETIC_NOISE_MULT`
+and `SYNTHETIC_NOISE_ADD_SD_FRACTION`. The latter sets additive noise as a
+fraction of the sample standard deviation of `x`.
+
+For a faster smoke test, reduce the replication counts with environment
+variables:
+
+```bash
+SYNTHETIC_BOOTSTRAPS=100 SYNTHETIC_MC_DRAWS=5000 SYNTHETIC_NOISE_REFITS=50 SYNTHETIC_NOISE_DRAWS=500 python examples/logistic_synthetic/run_synthetic_logistic.py
+```
+
+The example tests:
+
+- RAW and LOG logistic fitting and goodness-of-fit;
+- Wald, MCA, NPBS, and PBS intervals and pointwise confidence bands;
+- intervals for `x50` and `s50`;
+- local elasticity of `x50` and `s50`; and
+- additive and multiplicative measurement-noise propagation under fixed-model
+  and refitting analyses.
+
+The synthetic `TRIM` input is created deterministically by removing one
+high-valued NC observation. This is included only to exercise the same two-data
+set code paths as the clinical workflow. It does not imply that trimming
+improves a model or validates the FULL--TRIM analysis.

organized_uncertainty_analysis/examples/logistic_synthetic/independent_test_outputs/01_fit_gof/synthetic_logistic_fit_gof.csv

@@ -0,0 +1,5 @@
+Dataset,Predictor,theta_0,theta_1,LLF,NLL,AIC,BIC,A,n,k
+FULL,RAW,-5.175213918197551,0.09567979311017398,-58.431972215947795,58.431972215947795,120.86394443189559,127.01429206236324,0.83125,160,2
+FULL,LOG,-19.22407945964182,4.877273784207884,-58.95830957941189,58.95830957941189,121.91661915882378,128.06696678929143,0.825,160,2
+TRIM,RAW,-5.420311312754999,0.10129050120549274,-55.684851394921694,55.684851394921694,115.36970278984339,121.50751119428385,0.8364779874213837,159,2
+TRIM,LOG,-20.083923046756592,5.105373961812146,-56.579803576801844,56.579803576801844,117.15960715360369,123.29741555804415,0.8238993710691824,159,2

organized_uncertainty_analysis/examples/logistic_synthetic/independent_test_outputs/02_ci/synthetic_logistic_bootstrap_diagnostics.csv

@@ -0,0 +1,17 @@
+Panel,Method,attempted,successful,rejected,rejected_nonfinite,rejected_slope,rejected_x50,success_rate,failed,failed_or_rejected
+FULL-RAW,MC,20000,20000,0.0,0.0,0.0,0.0,1.0,,
+FULL-RAW,Nonparametric,100,100,,,,,,0.0,
+FULL-RAW,Stratified,100,100,,,,,1.0,0.0,
+FULL-RAW,Parametric,100,100,,,,,1.0,,0.0
+FULL-LOG,MC,20000,20000,0.0,0.0,0.0,0.0,1.0,,
+FULL-LOG,Nonparametric,100,100,,,,,,0.0,
+FULL-LOG,Stratified,100,100,,,,,1.0,0.0,
+FULL-LOG,Parametric,100,100,,,,,1.0,,0.0
+TRIM-RAW,MC,20000,20000,0.0,0.0,0.0,0.0,1.0,,
+TRIM-RAW,Nonparametric,100,100,,,,,,0.0,
+TRIM-RAW,Stratified,100,100,,,,,1.0,0.0,
+TRIM-RAW,Parametric,100,100,,,,,1.0,,0.0
+TRIM-LOG,MC,20000,20000,0.0,0.0,0.0,0.0,1.0,,
+TRIM-LOG,Nonparametric,100,100,,,,,,0.0,
+TRIM-LOG,Stratified,100,100,,,,,1.0,0.0,
+TRIM-LOG,Parametric,100,100,,,,,1.0,,0.0

organized_uncertainty_analysis/examples/logistic_synthetic/independent_test_outputs/02_ci/synthetic_logistic_parameter_ci.csv

@@ -0,0 +1,21 @@
+Panel,Method,b0_hat,b0_LCL,b0_UCL,b0_width,b1_hat,b1_LCL,b1_UCL,b1_width,x50_hat,x50_med,x50_LCL,x50_UCL,x50_width,SUV50_hat,SUV50_med,SUV50_LCL,SUV50_UCL,SUV50_width,s50_hat,s50_med,s50_LCL,s50_UCL,s50_width,transform,l2,B_used
+FULL-RAW,Wald,-5.175213918197551,-6.723492468949212,-3.62693536744589,3.096557101503322,0.09567979311017398,0.06796022642022778,0.12339935980012018,0.0554391333798924,54.088891185606585,54.088891185606585,49.29469837541613,58.88308399579704,9.588385620380905,54.088891185606585,54.088891185606585,49.29469837541613,58.88308399579704,9.588385620380905,0.023919948277543495,0.023919948277543495,0.016990056605059634,0.030849839950027356,0.013859783344967722,raw,1e-08,
+FULL-RAW,MC,-5.175213918197551,-6.718616170330993,-3.653884410862909,3.0647317594680836,0.09567979311017398,0.0681388797549532,0.12292532079742984,0.05478644104247664,54.088891185606585,54.10362635319867,49.09504166308694,59.193167070517774,10.098125407430835,54.088891185606585,54.10362635319867,49.09504166308694,59.193167070517774,10.098125407430835,0.023919948277543495,0.02393413012407085,0.0170347199387383,0.03073133019935746,0.01369661026061916,raw,1e-08,20000.0
+FULL-RAW,Nonparametric,-5.175213918197551,-7.566815680746197,-3.8665253869475635,3.7002902937986337,0.09567979311017398,0.07288068943882343,0.13633886462556022,0.06345817518673678,54.088891185606585,53.93640779834455,49.3040812881574,58.02830786741363,8.724226579256232,54.088891185606585,53.93640779834455,49.3040812881574,58.02830786741363,8.724226579256232,0.023919948277543495,0.024187611865273607,0.01822017235970586,0.034084716156390055,0.015864543796684196,raw,1e-08,100.0
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organized_uncertainty_analysis/examples/logistic_synthetic/independent_test_outputs/02_ci_final/synthetic_logistic_bootstrap_diagnostics.csv

@@ -0,0 +1,13 @@
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organized_uncertainty_analysis/examples/logistic_synthetic/independent_test_outputs/02_ci_final/synthetic_logistic_parameter_ci.csv

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organized_uncertainty_analysis/examples/logistic_synthetic/independent_test_outputs/03_elasticity/synthetic_logistic_elasticity.csv

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organized_uncertainty_analysis/examples/logistic_synthetic/notebook_outputs/synthetic_logistic_bootstrap_diagnostics.csv

@@ -0,0 +1,13 @@
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organized_uncertainty_analysis/examples/logistic_synthetic/notebook_outputs/synthetic_logistic_elasticity.csv

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organized_uncertainty_analysis/examples/logistic_synthetic/notebook_outputs/synthetic_logistic_fit_gof.csv

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organized_uncertainty_analysis/examples/logistic_synthetic/notebook_outputs/synthetic_logistic_parameter_ci.csv

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organized_uncertainty_analysis/examples/logistic_synthetic/outputs/synthetic_logistic_bootstrap_diagnostics.csv

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organized_uncertainty_analysis/examples/logistic_synthetic/outputs/synthetic_logistic_elasticity.csv

@@ -0,0 +1,5 @@
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