Groupe d’études et de recherche en analyse des décisions

Output Analysis for Markov Chain Monte Carlo

Galin Jones

Markov chain Monte Carlo is a method of producing a correlated sample from a target distribution. Features of the target distribution are then estimated using this sample. Thus a fundamental question in MCMC is: When should the sampling stop? That is, when have we achieved good estimates? I will introduce a method that stops the MCMC sampling when the width of a confidence interval is less than a user-specified value. Hence calculating Monte Carlo standard errors is a critical step in assessing the output of the simulation. In this talk I will give an overview of fixed-width methodology and methods for calculating Monte Carlo standard errors. The main results will be illustrated in several examples.