{ "cells": [ { "cell_type": "markdown", "id": "be915d56-9a8a-422b-9da4-d7ca37dd0b85", "metadata": { "id": "be915d56-9a8a-422b-9da4-d7ca37dd0b85" }, "source": [ "# Bayesian modelling\n", "\n", "Gamma and betaprime distribution:\n", "\n", "Ref:\n", " * https://docs.scipy.org/doc/scipy/tutorial/stats/continuous_gamma.html\n", " * https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.betaprime.html" ] }, { "cell_type": "markdown", "id": "c9aacace", "metadata": {}, "source": [ "## Common" ] }, { "cell_type": "code", "execution_count": 1, "id": "0ade8aaa", "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import scipy\n", "import pandas as pd\n", "\n", "import os\n", "\n", "import data_utils\n", "import bayesian" ] }, { "cell_type": "markdown", "id": "6fa3ccb1-05c0-4ab9-a74a-a4e20d1e38f8", "metadata": { "id": "6fa3ccb1-05c0-4ab9-a74a-a4e20d1e38f8" }, "source": [ "## Data" ] }, { "cell_type": "code", "execution_count": 2, "id": "c72c613c", "metadata": { "executionInfo": { "elapsed": 2756, "status": "ok", "timestamp": 1715067840744, "user": { "displayName": "Marija Delić", "userId": "03427129792104028391" }, "user_tz": -120 }, "id": "c72c613c", "tags": [] }, "outputs": [], "source": [ "results_path = \"./results\"\n", "if not os.path.exists(results_path): os.makedirs(results_path)\n", "\n", "data_path = \"../../data/\"\n", "suv_filename = os.path.join(data_path, \"suv_percentilesSLOthenUWM.mat\")\n", "flags_filename = os.path.join(data_path,\"flags_combined.mat\")\n", "normal_range_filename = os.path.join(data_path, \"normal_range.mat\")" ] }, { "cell_type": "code", "execution_count": 3, "id": "f5ffd7f6", "metadata": {}, "outputs": [], "source": [ "\"\"\"\n", "Loading all data\n", "\"\"\"\n", "suv_dict = scipy.io.loadmat(suv_filename)\n", "flags_dict = scipy.io.loadmat(flags_filename)\n", "normal_range_dict = scipy.io.loadmat(normal_range_filename)" ] }, { "cell_type": "code", "execution_count": 4, "id": "4dbb2f49", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "odds = 10.6\n", "ns = [53, 5]\n" ] } ], "source": [ "# get data\n", "perc = 95\n", "organ = \"lung\"\n", "\n", "x, y = data_utils.get_data(organ, perc, suv_dict, flags_dict)\n", "odds = len(x[y == 0])/len(x[y == 1]) # Prob(Y=0)/Prob(Y=1)\n", "xs = [x[y == i] for i in range(2)]\n", "ns = [len(e) for e in xs]\n", "\n", "print(f\"{odds = }\")\n", "print(f\"{ns = }\")\n" ] }, { "cell_type": "markdown", "id": "8c4a5c84-c72a-4b48-a92c-7e25f5b752fc", "metadata": { "id": "8c4a5c84-c72a-4b48-a92c-7e25f5b752fc" }, "source": [ "## Explore data" ] }, { "cell_type": "code", "execution_count": 5, "id": "9879854b", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0:(1.3076106366121545, 0.25845619452679225)\n", "1:(2.451199436187744, 0.870810277632464)\n" ] }, { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "\"\"\"\n", " Explore if data can be fitted by beta-prime\n", "\"\"\"\n", "# compare fit in plt\n", "fig, axs = plt.subplots(ncols = 2, figsize=(6*2,5))\n", "\n", "for i, (e, ax) in enumerate(zip(xs, axs)):\n", " distr = scipy.stats.norm\n", " \n", " # fit on full parameter space\n", " pars_single = distr.fit(e)\n", " print(f\"{i}:{pars_single}\")\n", "\n", " # compare fit and data histogram\n", " t = np.linspace(min(e), max(e), 100)\n", "\n", " ax.hist(e, density = True, label = \"data\")\n", " ax.plot(t, distr.pdf(t, *pars_single), label = \"fit\")\n", " \n", " ax.set_title(f\"group:{i}\")\n", " ax.legend()\n" ] }, { "cell_type": "code", "execution_count": 6, "id": "93bdd9e8", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0:[1.30761064 0.2584562 ]\n", "1:[2.4511996 0.87081004]\n" ] }, { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "\"\"\"\n", " Explore if data can be fitted by beta-prime\n", "\"\"\"\n", "pars = np.array([1.30761064, 0.2584562 , 2.4511996 , 0.87081004])\n", "\n", "# compare fit in plt\n", "fig, axs = plt.subplots(ncols = 2, figsize=(6*2,5))\n", "\n", "for i, (e, ax) in enumerate(zip(xs, axs)):\n", " distr = scipy.stats.norm\n", " \n", " # fit on full parameter space\n", " pars_single = pars[2*i:2*(i+1)] #distr.fit(e)\n", " print(f\"{i}:{pars_single}\")\n", "\n", " # compare fit and data histogram\n", " t = np.linspace(min(e), max(e), 100)\n", "\n", " ax.hist(e, density = True, label = \"data\")\n", " ax.plot(t, distr.pdf(t, *pars_single), label = \"fit\")\n", " \n", " ax.set_title(f\"group:{i}\")\n", " ax.legend()" ] }, { "cell_type": "markdown", "id": "a29519f9", "metadata": {}, "source": [ "## Fit" ] }, { "cell_type": "code", "execution_count": null, "id": "081c152b", "metadata": {}, "outputs": [], "source": [ "# for testing define distribution we want to use\n", "# normal is not a good distribution!\n", "distr = scipy.stats.norm\n", "\n", "# define logarithm of pdfs used on the Bayesian model\n", "bounds = [\n", " [(0.1, 100), (0.1, 100)], # group 0\n", " [(0.1, 100), (0.1, 100)] # group 1\n", " ]\n", "# log of pdf for all choice\n", "def log_pdfs(x, pars, choice = 2):\n", " \n", " logpdf = distr.logpdf\n", "\n", " match choice:\n", " case 0: return logpdf(x, pars[0], pars[1])\n", " case 1: return logpdf(x, pars[0], pars[1])\n", " \n", " return (logpdf(x, pars[0], pars[1]), logpdf(x, pars[2], pars[3]))\n", "\n", "\n", "def distr_sample(rng, pars, n, choice = 2):\n", " \n", " rvs = distr.rvs\n", "\n", " match choice:\n", " case 0: return rvs(pars[0], pars[1], size = n, random_state = rng)\n", " case 1: return rvs(pars[0], pars[1], size = n, random_state = rng)\n", " \n", " return np.concatenate((rvs(pars[0], pars[1], size = n[0], random_state = rng), \n", " rvs(pars[2], pars[3], size = n[1], random_state = rng)))\n", "\n", "# define Bayesian model instance\n", "BM = bayesian.BayesianModelRegression\n", "bm = BM(odds, log_pdfs, bounds, distr_sample)" ] }, { "cell_type": "code", "execution_count": 8, "id": "46484c9e", "metadata": {}, "outputs": [], "source": [ "# doing the fit\n", "res_fit = bm.fit(x,y)" ] }, { "cell_type": "code", "execution_count": 9, "id": "fa5fa70e", "metadata": {}, "outputs": [ { "data": { "application/vnd.microsoft.datawrangler.viewer.v0+json": { "columns": [ { "name": "index", "rawType": "int64", "type": "integer" }, { "name": "LLF", "rawType": "float64", "type": "float" }, { "name": "AIC", "rawType": "float64", "type": "float" }, { "name": "BIC", "rawType": "float64", "type": "float" }, { "name": "A", "rawType": "float64", "type": "float" }, { "name": "chi2", "rawType": "float64", "type": "float" }, { "name": "p-value(chi2)", "rawType": "float64", "type": "float" }, { "name": "n", "rawType": "int64", "type": "integer" }, { "name": "k", "rawType": "int64", "type": "integer" }, { "name": "dof", "rawType": "int64", "type": "integer" } ], "ref": "2471df9b-0fc6-4aa6-ae4e-840b32557956", "rows": [ [ "0", "-6.684329291238636", "21.368658582477273", "29.610430624662946", "0.9655172413793104", "19.73899320013926", "0.9999949020267289", "58", "4", "54" ] ], "shape": { "columns": 9, "rows": 1 } }, "text/html": [ "
\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
LLFAICBICAchi2p-value(chi2)nkdof
0-6.68432921.36865929.6104310.96551719.7389930.99999558454
\n", "
" ], "text/plain": [ " LLF AIC BIC A chi2 p-value(chi2) n k \\\n", "0 -6.684329 21.368659 29.610431 0.965517 19.738993 0.999995 58 4 \n", "\n", " dof \n", "0 54 " ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# table of goodness of fit measures\n", "pd.DataFrame([bm.goodness_of_fit(x, y, res_fit[\"pars\"])])" ] }, { "cell_type": "code", "execution_count": 10, "id": "46717697", "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# plotting fit and data\n", "fig, ax = plt.subplots(figsize=(7,5))\n", "\n", "# plot input data\n", "for i, lab in zip(np.arange(2), [\"NC\", \"AE\"]):\n", " ax.scatter(x[y == i], y[y == i], label = lab, zorder = 2.5)\n", "\n", "# plotting optimal model\n", "xp = np.linspace(min(x), max(x), 100)\n", "ax.plot(xp, bm.model(xp, res_fit[\"pars\"]), label = \"fit\")\n", "\n", "ax.set_xlabel(r\"$x = max_{visit} SUV(visit, p)$\")\n", "ax.set_ylabel(\"P(AE|X = x)\")\n", "\n", "ax.legend()\n", "\n", "plt.savefig(os.path.join(results_path, \"bayesian_fit.pdf\"))\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "a974ab00-e992-4de8-8a9f-431264fe376a", "metadata": { "id": "a974ab00-e992-4de8-8a9f-431264fe376a" }, "source": [ "## CI of models" ] }, { "cell_type": "code", "execution_count": 11, "id": "8386c0d0", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "boots:get_nonparam_boots_pars\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/home/horvat/Documents/work/medfiz/git/uncertainty_study/python/bayesian/bayesian.py:112: RuntimeWarning: overflow encountered in exp\n", " return np.sum(np.log(1 + np.exp(-S*F)))\n", "/home/horvat/venvs/base/lib/python3.12/site-packages/scipy/optimize/_numdiff.py:592: RuntimeWarning: invalid value encountered in subtract\n", " df = fun(x1) - f0\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "boots:get_nonparam_strat_boots_pars\n", "boots:get_param_boots_pars\n", "boots:get_param_strat_boots_pars\n" ] } ], "source": [ "# nr. of bootstrapped samples\n", "Nboots = 10**4\n", "\n", "labs = [\"non-param\", \n", " \"non-param strat\", \n", " \"param\", \n", " \"param strat\"]\n", "\n", "funs = [\"get_nonparam_boots_pars\",\n", " \"get_nonparam_strat_boots_pars\", \n", " \"get_param_boots_pars\",\n", " \"get_param_strat_boots_pars\"]\n", "\n", "# defining twosided probabilities\n", "alpha = 0.05 # significance level\n", "probs = [alpha/2, 1 - alpha/2]\n", "\n", "# calculate bootstrapped parameters\n", "dict_bpars = dict()\n", "\n", "for lab, fun in zip(labs, funs):\n", " print(f\"boots:{fun}\")\n", " \n", " # define bootstrapping function \n", " qm = eval(f\"bm.{fun}\")\n", " \n", " # do bootstrapping\n", " dict_bpars[lab] = qm(x, y, Nboots)\n" ] }, { "cell_type": "code", "execution_count": 12, "id": "506a1d8d", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "non-param:\n", " isnan: []\n", " isinf: []\n", "non-param strat:\n", " isnan: []\n", " isinf: []\n", "param:\n", " isnan: []\n", " isinf: []\n", "param strat:\n", " isnan: []\n", " isinf: []\n" ] } ], "source": [ "# checking if we have strange parameters\n", "for lab, bpars in dict_bpars.items():\n", " print(f\"{lab}:\")\n", " print(\" isnan:\", [p for p in bpars if np.isnan(p).any()])\n", " print(\" isinf:\", [p for p in bpars if np.isinf(p).any()])" ] }, { "cell_type": "code", "execution_count": 13, "id": "95681175", "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# plotting fit and data\n", "fig, ax = plt.subplots(figsize=(7,5))\n", "\n", "# plot input data\n", "for i, lab in zip(np.arange(2), [\"NC\", \"AE\"]):\n", " ax.scatter(x[y == i], y[y == i], label = lab, zorder = 2.5)\n", "\n", "# plotting optimal model\n", "xp = np.linspace(min(x), max(x), 100)\n", "ax.plot(xp, bm.model(xp, res_fit[\"pars\"]), label = \"fit\")\n", "\n", "# plotting CI\n", "for lab, bpars in dict_bpars.items():\n", "\n", " # calculate model values of for all bootstrapped parameters\n", " model_values = [bm.model(xp, p) for p in bpars]\n", " qs = np.quantile(model_values, probs, axis = 0)\n", "\n", " # make plot of quantiles\n", " ax.fill_between(xp, *qs, alpha = 0.2, label = f\"CI:{lab}\")\n", "\n", "ax.set_xlabel(r\"$x = max_{visit} SUV(visit, p)$\")\n", "ax.set_ylabel(\"P(AE|X = x)\")\n", "\n", "ax.legend()\n", "\n", "plt.savefig(os.path.join(results_path, \"bayesian_CI_cmp.pdf\"))\n", "plt.show()" ] } ], "metadata": { "colab": { "provenance": [] }, "kernelspec": { "display_name": "base", "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": "3.12.3" } }, "nbformat": 4, "nbformat_minor": 5 }