File size: 2,089 Bytes
3b0d6b3 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 | 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],
}
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