An automated stopping rule for MCMC convergence assessment
A new methodological approach for assessing convergence of Markov chain Monte Carlo algorithms is proposed. This approach is based on the fact that normality is an implication of sufficient mixing, which is testable across parallel sequences issued from a dispersed initial distribution, and allows for controlling precision. Instead of checking for stationarity of ergodic Markov chains, it is primarily aimed at controlling the precision of estimates of averaged sums. A natural way to do this is through confidence regions based on normal approximation resulting from the central limit theorem (CLT) for Markov chains. Difficulties arise since one has to make use of two asymptotic results, the CLT and the convergence to the limiting variance. This is the reason why it is proposed, first, to use statistical tests for testing normality of the normalized sums, using samples obtained from parallel chains, and second, to monitor variance stabilization. Both methods work without knowledge on the sampler driving the chain, and the normality diagnostic leads to automated stopping rules. These stopping rules are implemented in a software toolbox whose performances are illustrated through simulations for finite and continuous state chains reflecting some typical situations and a full scale application. Comparisons are made with the binary control method of Raftery and Lewis.
scientific article; zbMATH DE number 1452446