Positivity of hit-and-run and related algorithms

Abstract

We prove positivity of the Markov operators that correspond to the hit-and-run algorithm, random scan Gibbs sampler, slice sampler and an Metropolis algorithm with positive proposal. In all of these cases the positivity is independent of the state space and the stationary distribution. In particular, the results show that it is not necessary to consider the lazy versions of these Markov chains. The proof relies on a well known lemma which relates the positivity of the product M T M^*, for some operators M and T, to the positivity of T. It remains to find that kind of representation of the Markov operator with a positive operator T.

References in corpus (1)

• Rapid mixing of Swendsen-Wang and single-bond dynamics in two dimensions

Cited by in corpus (8)

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• Convergence of hybrid slice sampling via spectral gap
• Error bounds of MCMC for functions with unbounded stationary variance
• Discrepancy estimates for variance bounding Markov chain quasi-Monte Carlo
• Computation of expectations by Markov chain Monte Carlo methods
• Efficient implementation of Markov chain Monte Carlo when using an unbiased likelihood estimator
• Comparison of hit-and-run, slice sampling and random walk Metropolis