Read a Bootstrap Percentile Interval as a Method Choice

Name the interval construction

A bootstrap distribution contains repeated estimates computed from resampled data. Different interval methods use that distribution differently. A percentile interval takes specified quantiles directly from the bootstrap estimates; a normal approximation uses an estimated standard error, while other methods apply additional corrections.

The SciPy bootstrap reference documents percentile, basic and BCa options. State the chosen method explicitly. A report saying only “bootstrap 95% CI” leaves an important analytical choice unresolved.

Inspect the distribution before its endpoints

Check whether estimates are finite, whether optimization failed and whether the distribution has strong skew, repeated boundary values or disconnected regions. Record the resampling unit and confirm that the statistic is calculated consistently in every replicate. A long list of numbers is not necessarily a valid approximation to the desired sampling uncertainty.

Do not silently discard failed replicates. Investigate their cause and specify how failure affects the target analysis. Generating more replicates may reduce Monte Carlo noise but will not fix a systematic fitting or resampling error.

Work through a hypothetical percentile result

Suppose a valid resampling procedure produces 10,000 finite estimates of a difference. The empirical 2.5th and 97.5th percentiles are −1.2 and 3.8 units. The reported percentile interval is therefore [−1.2, 3.8]; it is not constructed by adding and subtracting those values from the original estimate.

If the original estimate is 1.0, the two endpoint distances are 2.2 and 2.8 units. That asymmetry is compatible with a percentile construction. It should not be “corrected” to a symmetric interval merely for presentation. Record the quantile convention when exact reproduction of endpoints matters.

Assess computational stability

Repeat the procedure with an independent random stream or add replicates under a planned check, then compare endpoint movement. Large changes may indicate insufficient simulation precision or an unstable statistic. Small changes establish numerical stability for the observed data and method, not guaranteed coverage in every population.

Explain limitations for very small samples, extreme quantiles or statistics near boundaries. Keep the interval in the correct units and distinguish it from a prediction interval for a future observation. The final result should state the statistic, resampling design, replicate count, interval method and handling of failures so another analyst can reproduce both the calculation and its qualifications.

Source verification: 6 November 2026. Examples are hypothetical.