Clarify pointwise confidence band coverage

notebooks/logit_all_models.ipynb

@@ -571,7 +571,9 @@
    "id": "32deb7403fd0",
    "metadata": {},
    "source": [
-    "### 2.2 Fitted risk curve and confidence bands\n"
+    "### 2.2 Fitted risk curve and confidence bands\n",
+    "\n",
+    "**Coverage note.** The term *confidence band* is used in its standard graphical sense. The displayed limits are pointwise confidence intervals evaluated separately at each predictor value; they do not provide simultaneous coverage of the complete fitted curve.\n"
    ]
   },
   {
@@ -1181,7 +1183,9 @@
    "id": "8029f7f521b1",
    "metadata": {},
    "source": [
-    "### 3.2 Fitted risk curve and confidence bands\n"
+    "### 3.2 Fitted risk curve and confidence bands\n",
+    "\n",
+    "**Coverage note.** The displayed limits are pointwise confidence intervals evaluated separately at each predictor value; they are not simultaneous confidence bands for the complete curve.\n"
    ]
   },
   {
@@ -2148,7 +2152,9 @@
    "id": "6ad4c94ba24a",
    "metadata": {},
    "source": [
-    "### 4.3 Fitted risk curve and asymptotic confidence bands\n"
+    "### 4.3 Fitted risk curve and asymptotic confidence bands\n",
+    "\n",
+    "**Coverage note.** The displayed limits are pointwise confidence intervals evaluated separately at each predictor value; they are not simultaneous confidence bands for the complete curve.\n"
    ]
   },
   {
@@ -2222,7 +2228,9 @@
    "id": "32da73e5cac3",
    "metadata": {},
    "source": [
-    "### 4.4 Model confidence-interval comparison\n"
+    "### 4.4 Model confidence-interval comparison\n",
+    "\n",
+    "**Coverage note.** All analytic and bootstrap envelopes compared below are pointwise in the predictor. Their nominal coverage applies at a fixed predictor value, not simultaneously over the complete curve.\n"
    ]
   },
   {

notebooks/logit_mono-cubic4paper.ipynb

@@ -7062,7 +7062,9 @@
    "id": "67fa2c6c",
    "metadata": {},
    "source": [
-    "##  Model CI"
+    "##  Model CI\n",
+    "\n",
+    "**Coverage note.** We use *confidence band* as the standard graphical term for the envelope around the fitted function. The limits calculated below are pointwise confidence intervals: their nominal coverage applies separately at each fixed predictor value and not simultaneously to the complete curve.\n"
    ]
   },
   {

notebooks/logit_review_boots.ipynb

@@ -1450,7 +1450,9 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "## Comparison of confidence bands"
+    "## Comparison of confidence bands\n",
+    "\n",
+    "**Coverage note.** The analytic and bootstrap envelopes below are pointwise confidence intervals evaluated separately at each predictor value. Although they are called confidence bands graphically, they do not provide simultaneous coverage of the complete fitted curve.\n"
    ]
   },
   {