Rigorous determination of the optimal block-bootstrap length

Determine a universally rigorous method for selecting the optimal block length in block-bootstrap resampling of the autocorrelated lattice QCD data.

Background

The analysis uses non-overlapping block bootstrap resampling because the lattice QCD configurations are strongly autocorrelated near a first-order phase transition. The authors select a block length empirically by examining a smoothed noise-to-signal diagnostic and use a value near 400 for the present dataset.

They explicitly acknowledge that this heuristic does not establish stationarity or optimality. A general, rigorous procedure for determining the optimal block size remains unresolved, and the reported uncertainties are conditional on the empirically selected block length.

References

In general, the determination of an optimal block size remains a difficult problem, and no universally rigorous method has yet been established.

— Bias-Corrected Machine-Learning Estimation of Chiral Condensate Cumulants: A Retrospective Lattice QCD Case Study  (2608.30416 - Choi et al., 31 Aug 2026) in Appendix, Section "Block Bootstrap resampling" (Section \ref{sec:block-bs})