| from __future__ import annotations |
|
|
| import math |
| import random |
|
|
|
|
| def wilson_interval(successes: int, n: int, confidence: float = 0.95) -> tuple[float, float]: |
| if n <= 0: |
| return 0.0, 0.0 |
| z = 1.959963984540054 |
| phat = successes / n |
| denom = 1 + z * z / n |
| center = (phat + z * z / (2 * n)) / denom |
| margin = z * math.sqrt((phat * (1 - phat) + z * z / (4 * n)) / n) / denom |
| return max(0.0, center - margin), min(1.0, center + margin) |
|
|
|
|
| def bootstrap_ci(values: list[float], iterations: int = 2000, confidence: float = 0.95) -> tuple[float, float]: |
| if not values: |
| return 0.0, 0.0 |
| if len(values) == 1: |
| return values[0], values[0] |
| means = [] |
| for _ in range(iterations): |
| sample = [random.choice(values) for _ in range(len(values))] |
| means.append(sum(sample) / len(sample)) |
| means.sort() |
| alpha = (1 - confidence) / 2 |
| lo_idx = max(0, int(alpha * len(means))) |
| hi_idx = min(len(means) - 1, int((1 - alpha) * len(means)) - 1) |
| return means[lo_idx], means[hi_idx] |
|
|
|
|
| def task_bootstrap_ci(task_values: list[float], iterations: int = 2000, confidence: float = 0.95) -> tuple[float, float]: |
| return bootstrap_ci(task_values, iterations=iterations, confidence=confidence) |
|
|
|
|
| def paired_bootstrap_delta( |
| left: list[float], right: list[float], iterations: int = 2000, confidence: float = 0.95 |
| ) -> dict: |
| if not left or not right or len(left) != len(right): |
| return {"delta": 0.0, "ci_low": 0.0, "ci_high": 0.0} |
| deltas = [] |
| paired = list(zip(left, right)) |
| for _ in range(iterations): |
| sample = [random.choice(paired) for _ in range(len(paired))] |
| diffs = [l - r for l, r in sample] |
| deltas.append(sum(diffs) / len(diffs)) |
| deltas.sort() |
| alpha = (1 - confidence) / 2 |
| lo_idx = max(0, int(alpha * len(deltas))) |
| hi_idx = min(len(deltas) - 1, int((1 - alpha) * len(deltas)) - 1) |
| observed = sum(l - r for l, r in paired) / len(paired) |
| return { |
| "delta": observed, |
| "ci_low": deltas[lo_idx], |
| "ci_high": deltas[hi_idx], |
| } |
|
|
