Bootstrap Confidence Interval
A Bootstrap Confidence Interval estimates the sampling distribution of a statistic (e.g. Sharpe) by repeatedly resampling the observed trade sequence with replacement and computing the statistic on each resample.
The math
B resamples → {θ̂₁*, θ̂₂*, ..., θ̂_B*} → percentile CI: [θ̂*(α/2), θ̂*(1−α/2)]B = number of resamples (Pancake uses 10,000), θ̂* = statistic computed on each resample, α = significance level (0.05 for 95% CI).
Why it matters
Sharpe and Sortino have known analytical confidence intervals under normality, but prediction-market return distributions are rarely normal. Bootstrap makes no distributional assumption — it lets the data speak. Efron (1979) introduced bootstrap as a general alternative to jackknife; it has since become the default for non-parametric inference.
Bootstrap resamples treat trades as independent — serial correlation in returns (e.g. from trend-following) can cause the CI to be too narrow. Block bootstrap can address this but is not currently used in Pancake. Bootstrap CIs also require a reasonable N: below ~20 trades, even 10,000 resamples cannot correct for a sparse sample.
Published source
Efron, B. (1979). "Bootstrap Methods: Another Look at the Jackknife." Annals of Statistics, 7(1), 1–26.