MARKOV-NORMAL ANALYSIS OF ITERATIVE SIMULATIONS BEFORE THEIR CONVERGENCE

Iterative simulation techniques are becoming standard tools in Bayesia n statistics, a notable example being the Gibbs sampler, whose draws f orm a Markov chain. Standard practice is to run the simulation until c onvergence is approached in the sense of the draws appearing to be sta tionary. At this point, the set of stationary draws can be used to pro vide an estimate of the target distribution. However, when the distrib utions involved are normal and the draws form a Markov chain, the targ et distribution can be reliably estimated by maximum likelihood (ML) u sing draws before their convergence to the target distribution. This f act suggests that the normal-based ML estimates can be exploited to es timate the mean and covariance matrix of an approximately normal targe t distribution before convergence is reached, and that these estimates call be used to define a restarting distribution for the simulation. Here, we describe the needed technology and explore its relevance to p ractice. The tentative conclusion is that the Markov-Normal restarting procedure can be computationally advantageous when the target distrib ution is nearly normal, especially in massively parallel or distribute d computing environments where many sequences can be run for the same effective cost as one sequence.