A table of short-period Tausworthe generators for Markov chain quasi-Monte Carlo

Abstract

We consider the problem of estimating expectations by using Markov chain Monte Carlo methods and improving the accuracy by replacing IID uniform random points with quasi-Monte Carlo (QMC) points. Recently, it has been shown that Markov chain QMC remains consistent when the driving sequences are completely uniformly distributed (CUD). However, the definition of CUD sequences is not constructive, so an implementation method using short-period Tausworthe generators (i.e., linear feedback shift register generators over the two-element field) that approximate CUD sequences has been proposed. In this paper, we conduct an exhaustive search of short-period Tausworthe generators for Markov chain QMC in terms of the $t$-value, which is a criterion of uniformity widely used in the study of QMC methods. We provide a parameter table of Tausworthe generators and show the effectiveness in numerical examples using Gibbs sampling.

References in corpus (5)

• Three discussions of the paper "sequential quasi-Monte Carlo sampling", by M. Gerber and N. Chopin
• Consistency of Markov chain quasi-Monte Carlo on continuous state spaces
• Construction of weakly CUD sequences for MCMC sampling
• Discrepancy estimates for variance bounding Markov chain quasi-Monte Carlo
• Characterization of matrices $B$ such that $(I,B,B^2)$ generates a digital net with $t$-value zero

Cited by in corpus (1)

• A search for short-period Tausworthe generators over ${\mathbb{F}}_b$ with application to Markov chain quasi-Monte Carlo