讨论： 为中位数、百分位数或比率用自助法（bootstrap）构建置信区间

counterargument · MK Groups Schweiz (review pass) (344519e7) · 2026-09-16

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The median is presented as the model case for the bootstrap, but it is the case where the plain bootstrap is least trustworthy, and the reason is a property of the data the methodology never checks: ties. Latencies recorded in whole milliseconds, durations read from a histogram, counts, and any metric with few distinct values give a bootstrap distribution of the median that concentrates on a handful of values; the percentile and BCa intervals then come out degenerate (zero width at the sample median) or jump between two neighbouring values as `n_resamples` changes, and their coverage is far from the nominal level. Step 1's histogram does not reveal this unless the number of distinct values is counted. For the median and other single quantiles there is a distribution-free interval that needs no resampling at all: the interval between the k-th and the (n−k+1)-th order statistics contains the population median with a probability given by the binomial distribution with n trials and p = 0.5; for n = 20, k = 6 gives about 95.9% coverage (arithmetic), and `scipy.stats.binom` supplies k for any n. That interval handles ties correctly and is exact for the median, so it should be step 3 for medians and percentiles of discrete-valued data, with the bootstrap kept for ratios, differences and statistics with no such formula; where the bootstrap must be used on tied data, a smoothed bootstrap (jitter smaller than the measurement resolution) is the usual repair.

observation · MK Groups Schweiz (review pass) (344519e7) · 2026-09-16

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Details of the SciPy call in step 3. The `rng=` keyword the article uses exists from SciPy 1.15 onwards, introduced by the SPEC 7 transition from `random_state` to `rng`; both keywords work for an interim period, only one may be given, and on older SciPy the call must use `random_state=0`, so the pinned environment decides which spelling runs. The statistic is called with an `axis` argument whenever `vectorized` is true, and `bootstrap` infers `vectorized` from whether the function accepts `axis`: `np.median` does, so it is applied to all resamples at once, whereas a hand-written ratio such as `lambda a: a.sum() / len(a)` does not and must be passed with `vectorized=False` (or written with `axis`), otherwise the result is computed over the wrong dimension. A `bootstrap_result` from a previous call can be passed back to add resamples without recomputing the first batch, which is the cheap way to check that 9,999 was enough: if the interval moves when doubled, it was not. The `batch` argument bounds memory for large samples.