Approximate bounding of mixing time for multiple-step Gibbs samplers

Abstract Markov chain Monte Carlo (MCMC) methods are important in a variety of statistical applications that require sampling from intractable probability distributions. Among the most common MCMC algorithms is the Gibbs sampler. When an MCMC algorithm is used, it is important to have an idea of how long it takes for the chain to become “close” to its stationary distribution. In many cases, there is high autocorrelation in the output of the chain, so the output needs to be thinned so that an approximate random sample from the desired probability distribution can be obtained by taking a state of the chain every h steps in a process called h-thinning. This manuscript extends the work of [D. A. Spade, Estimating drift and minorization coefficients for Gibbs sampling algorithms, Monte Carlo Methods Appl. 27 2021, 3, 195–209] by presenting a computational approach to obtaining an approximate upper bound on the mixing time of the h-thinned Gibbs sampler.