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arXiv · 2409.11379

Bootstrap-determined p-values in Lattice QCD

Norman Christ·Rajiv Eranki·Christopher Kelly
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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 $\chi^2$ statistic do not apply, such as for uncorrelated fits. Specifically, we analyze a general alternative to the correlated $\chi^2$ statistic referred to as $q^2$, 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.

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Norman Christ, Rajiv Eranki, Christopher Kelly. 2024-09-17. Bootstrap-determined p-values in Lattice QCD. https://arxiv.org/abs/2409.11379

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