Andrew L. Nguyen

Regenerative Markov Chain Monte Carlo for Any Distribution

While Markov chain Monte Carlo (MCMC) methods are frequently used for difficult calculations in a wide range of scientific disciplines, they suffer from a serious limitation: their samples are not independent and identically distributed. Consequently, estimates of expectations are biased if the initial value of the chain is not drawn from the target distribution. Regenerative simulation provides an elegant solution to this problem. In this article, we propose a simple regenerative MCMC algorithm to generate variates for any distribution.

Regenerative Markov Chain Importance Sampling

ABSTRACT We introduce Markov Chain Importance Sampling (MCIS), which combines importance sampling (IS) and Markov Chain Monte Carlo (MCMC) to estimate some characteristics of a non-normalized multi-dimensional distribution. Especially, we introduce some importance functions whose variates are regeneratively generated by MCMC; these variates then are used to estimate the quantity of interest through IS. Because MCIS is regenerative, it overcomes the burn-in problem associated with MCMC. It could also speed up the mixing rate in MCMC.