fix(#125): fail closed on degenerate BCa intervals

src/liouscope/fitting/bootstrap.py

@@ -13,6 +13,7 @@
 
 from __future__ import annotations
 
+import warnings
 from collections.abc import Callable
 
 import numpy as np
@@ -168,6 +169,14 @@ def bca_ci(
 
     Returns ``(p, 2)`` array of ``(lo, hi)`` per parameter at level
     ``1 - alpha``.
+
+    A parameter whose bootstrap distribution is degenerate, or whose adjusted
+    quantiles collapse to an exactly zero-width interval, is reported as
+    ``(NaN, NaN)`` with a warning. This follows the fail-closed semantics used
+    by SciPy's BCa implementation for degenerate bootstrap distributions:
+    arithmetic concentration is not promoted to a claim of perfect certainty
+    when the resampling model contains no measurable spread (issue #125).
+    Other non-degenerate parameters in the same fit remain reportable.
     """
     samples = np.asarray(samples, dtype=float)
     theta_hat = np.asarray(theta_hat, dtype=float)
@@ -177,6 +186,16 @@ def bca_ci(
     z_alpha_hi = ndtri(1.0 - alpha / 2.0)
     for j in range(p):
         boot_j = np.sort(samples[:, j])
+        if boot_j.size == 0 or np.all(boot_j == boot_j[0]):
+            warnings.warn(
+                f"bca_ci: bootstrap distribution for parameter {j} is "
+                "degenerate; uncertainty is unavailable rather than a "
+                "zero-width confidence claim (issue #125)",
+                RuntimeWarning,
+                stacklevel=2,
+            )
+            cis[j] = (float("nan"), float("nan"))
+            continue
         # Bias-correction z0 with half-correction for ties (Efron 1987, S3
         # audit 2026-06-04). Using a strict ``<`` only would send the
         # proportion to 0 (hence z0 -> -inf, clamped) whenever many bootstrap
@@ -214,6 +233,16 @@ def adjusted(z_alpha: float, z0_: float = z0, a_: float = a) -> float:
         # continuous-percentile estimator.
         lo = float(np.quantile(boot_j, q_lo, method="linear"))
         hi = float(np.quantile(boot_j, q_hi, method="linear"))
+        if lo == hi:
+            warnings.warn(
+                f"bca_ci: confidence interval for parameter {j} collapsed to "
+                "exactly zero width; uncertainty is unavailable rather than "
+                "perfectly known (issue #125)",
+                RuntimeWarning,
+                stacklevel=2,
+            )
+            cis[j] = (float("nan"), float("nan"))
+            continue
         cis[j] = (lo, hi)
     return cis
 

tests/test_issue125_degenerate_bca.py

@@ -0,0 +1,57 @@
+"""Regression tests for issue #125: degenerate BCa uncertainty claims."""
+
+from __future__ import annotations
+
+import numpy as np
+import pytest
+
+from liouscope.fitting.bootstrap import bca_ci
+
+
+def test_degenerate_bootstrap_distribution_is_unavailable_not_zero_width() -> None:
+    samples = np.ones((200, 1), dtype=float)
+    theta_hat = np.array([1.0])
+
+    with pytest.warns(RuntimeWarning, match="degenerate"):
+        ci = bca_ci(samples, theta_hat)
+
+    assert np.isnan(ci[0, 0])
+    assert np.isnan(ci[0, 1])
+
+
+def test_degenerate_parameter_does_not_withhold_an_independent_parameter() -> None:
+    x = np.linspace(-1.0, 1.0, 200)
+    samples = np.column_stack([np.ones_like(x), x])
+    theta_hat = np.array([1.0, 0.0])
+
+    with pytest.warns(RuntimeWarning, match="parameter 0"):
+        ci = bca_ci(samples, theta_hat)
+
+    assert np.all(np.isnan(ci[0]))
+    assert np.all(np.isfinite(ci[1]))
+    assert ci[1, 0] < ci[1, 1]
+
+
+def test_ordinary_nondegenerate_distribution_keeps_a_finite_interval() -> None:
+    rng = np.random.default_rng(125)
+    samples = rng.normal(loc=0.7, scale=0.03, size=(1000, 1))
+    theta_hat = np.array([0.7])
+
+    ci = bca_ci(samples, theta_hat)
+
+    assert np.all(np.isfinite(ci))
+    assert ci[0, 0] < ci[0, 1]
+    assert ci[0, 0] < theta_hat[0] < ci[0, 1]
+
+
+def test_zero_width_after_adjusted_quantiles_is_not_reported_as_certainty() -> None:
+    # Non-identical distribution, but >97.5% of its mass sits on one value.
+    # The BCa adjusted endpoints can therefore collapse to that value. The
+    # claim boundary, not merely the raw distribution, must catch the collapse.
+    samples = np.concatenate([np.ones(199), np.array([2.0])]).reshape(-1, 1)
+    theta_hat = np.array([1.0])
+
+    with pytest.warns(RuntimeWarning, match="zero width"):
+        ci = bca_ci(samples, theta_hat)
+
+    assert np.all(np.isnan(ci[0]))