ADAPTIVE MARKOV CHAIN MONTE CARLO CONFIDENCE INTERVALS

Abstract. In Adaptive Markov Chain Monte Carlo (AMCMC) simulation, classical estimators of asymptotic variances are inconsistent in general. In this work we establish that despite this inconsistency, confidence interval procedures based on these estimators remain consistent. We study two classes of confidence intervals, one based on the standard Gaussian limit theory, and the class of so-called fixed-b confidence intervals. We compare the two procedures by deriving upper bounds on their convergence rates. We establish that the rate of convergence of fixed-b variance estimators is at least log(n)/ n, while the convergence rate of the classical procedure is typically of order n−1/3. We use simulation examples to illustrate the results. 1