Statistica Sinica

Chuanhai Liu and Donald B. Rubin

Abstract:Inference using simulation has become a dominant theme in modern statistics, whether using the bootstrap to simulate sampling distributions of statistics, Markov chain Monte Carlo to simulate posterior distributions of parameters, or multiple imputation to simulate the posterior predictive distribution of missing values. Inference via simulations can, in some cases, be greatly facilitated by accompanying methods of analysis based on more traditional mathematical statistical techniques. Here we illustrate this point using one example of such technology: the analysis, based on a Markov-normal model of the stationary distribution underlying an iterative simulation, of parallel simulations before their convergence, thereby allowing a redesign of the simulation for better performance. The potential value of this approach is documented using an example involving censored data.

Key words and phrases:Bayesian methods, the CA-DA algorithm, the DA algorithm, the EM algorithm, the Gibbs sampler, Markov chain Monte Carlo, maximum likelihood estimation, multiple imputation, the PX-EM algorithm.