MCMC Convergence Diagnostic Via The Central Limit Theorem

. Markov Chain Monte Carlo (MCMC) methods, as introduced by Gelfand and Smith (1990), provide a simulation based strategy for statistical inference. The application fields related to these methods, as well as theoretical convergence properties, have been intensively studied in the recent literature. However, many improvements are still expected to provide workable and theoretically well-grounded solutions to the problem of monitoring the convergence of actual outputs from MCMC algorithms (i.e. the convergence assessment problem) . In this paper, we introduce and discuss a methodology based on the Central Limit Theorem for Markov chains to assess convergence of MCMC algorithms. Instead of searching for approximate stationarity, we primarily intend to control the precision of estimates of the invariant probability measure, or of integrals of functions with respect to this measure, through confidence regions based on normal approximation. The first proposed control method tests the normal..