STUDYING CONVERGENCE OF MARKOV-CHAIN MONTE-CARLO ALGORITHMS USING COUPLED SAMPLE PATHS

I describe a simple procedure for investigating the convergence proper ties of Markov chain Monte Carlo sampling schemes. The procedure uses coupled chains from the same sampler, obtained by using the same seque nce of random deviates for each run. By examining the distribution of the iteration at which all sample paths couple, convergence properties for the system can be established. The procedure also provides a simp le diagnostic for detecting modes in multimodal posteriors. Several ex amples of the procedure are provided. In Ising models, the relation be tween the correlation parameter and the convergence rate of rudimentar y Gibbs samplers is investigated. In another example, the effects of m ultiple modes on the convergence of coupled paths are explored using m ixtures of bivariate normal distributions. The technique is also used to evaluate the convergence properties of a Gibbs sampling scheme appl ied to a model for rat growth rates.