Proceedings of the 1998 Winter Simulation Conference

In simulation modeling and analysis, there are two situations where there is uncertainty about the number of parameters needed to specify a model. The first is in input modeling where real data is being used to fit a finite mixture model and where there is uncertainty about the number of components in the mixture. Secondly, at the output analysis stage, it may be that a regression model is to be fitted to the simulation output, where the number of terms, and hence the number of parameters, is unknown. In statistical terms, such problems are non-standard and require special handling. One way is to use a Bayesian Markov Chain Monte Carlo (MCMC) analysis. Such a method has been suggested by George and McCulloch(1993) using a hierarchical Bayesian model. This method is flexible, but does introduce many additional parameters. This tends to make the modelling look rather complicated. In this paper we adopt a classical Bayesian approach that is essentially equivalent to the George and McCulloch technique, but that has a much less elaborate structure and which renders model interpretation much simpler. The method is illustrated by a regression metamodel example.