MARKOV-CHAIN MONTE-CARLO IN PRACTICE - A ROUND-TABLE DISCUSSION

Markov chain Monte Carlo (MCMC) methods make possible the use of flexi ble Bayesian models that would otherwise be computationally infeasible . In recent years, a great variety of such applications have been desc ribed in the literature. Applied statisticians who are new to these me thods may have several questions and concerns, however: How much effor t and expertise are needed to design and use a Markov chain sampler? H ow much confidence can one have in the answers that MCMC produces? How does the use of MCMC affect the rest of the model-building process? A t the Joint Statistical Meetings in August, 1996, a panel of experienc ed MCMC users discussed these and other issues, as well as various ''t ricks of the trade.'' This article is an edited recreation of that dis cussion. Its purpose is to offer advice and guidance to novice users o f MCMC-and to not-so-novice users as well. Topics include building con fidence in simulation results, methods for speeding and assessing conv ergence, estimating standard errors, identification of models for whic h good MCMC algorithms exist, and the current state of software develo pment.