Statistical analysis method for the worldvolume hybrid Monte Carlo algorithm

TL;DR

This paper develops a statistical analysis framework for the worldvolume hybrid Monte Carlo algorithm, demonstrating its Markov chain properties and autocorrelation behavior, with numerical validation on a random matrix model.

Contribution

It proves the Markov property for subsamples in the WV-HMC algorithm and investigates the autocorrelation scaling law across subregions.

Findings

Subsamples in the WV-HMC are Markov chains.

Autocorrelation time scales linearly with subregion probability.

Numerical confirmation in a chiral random matrix model.

Abstract

We discuss the statistical analysis method for the worldvolume hybrid Monte Carlo (WV-HMC) algorithm [arXiv:2012.08468], which was recently introduced to substantially reduce the computational cost of the tempered Lefschetz thimble method. In the WV-HMC algorithm, the configuration space is a continuous accumulation (worldvolume) of deformed integration surfaces, and sample averages are considered for various subregions in the worldvolume. We prove that, if a sample in the worldvolume is generated as a Markov chain, then the subsample in the subregion can also be regarded as a Markov chain. This ensures the application of the standard statistical techniques to the WV-HMC algorithm. We particularly investigate the autocorrelation times for the Markov chains in various subregions, and find that there is a linear relation between the probability to be in a subregion and the autocorrelation time for the corresponding subsample. We numerically confirm this scaling law for a chiral random matrix model.