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DOE OSTI · 2559021

Bootstrap-determined p values in lattice QCD

Christ, N. H.·Eranki, R.·Kelly, C. (ORCID:0000000330331196)
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Abstract

We present a general method to determine the probability that stochastic Monte Carlo data, in particular those generated in a lattice QCD calculation, would have been obtained were that data drawn from the distribution predicted by a given theoretical hypothesis. Such a probability, or p -value, is often used as an important heuristic measure of the validity of that hypothesis. The proposed method offers the benefit that it remains usable in cases where the standard Hotelling T 2 methods based on the conventional χ 2 statistic do not apply, such as for uncorrelated fits. Specifically, we analyze q 2 , defined as the correlated χ 2 statistic obtained using an arbitrary covariance matrix estimator, and show how to use the bootstrap as a data-driven method to determine the expected distribution of q 2 for a given hypothesis with minimal assumptions. This distribution can then be used to determine the p -value for a fit to the data. We also describe a bootstrap approach for quantifying the impact upon this p -value of estimating population parameters from a single ensemble of N samples. The overall method is accurate up to a 1 / N bias which we do not attempt to quantify. Published by the American Physical Society 2025

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71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS

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Christ, N. H., Eranki, R., Kelly, C. (ORCID:0000000330331196). 2025-04-17. Bootstrap-determined p values in lattice QCD. https://doi.org/10.1103/physrevd.111.074514

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