Regression metamodeling in simulation using Bayesian methods

Further develops some of the ideas set out previously by the author (1998 Winter Simulation Conf., pp. 653-59, 1998) for output analysis using Bayesian Markov-chain Monte-Carlo (MCMC) techniques, when a regression metamodel is to be fitted to simulation output. The particular situation addressed in the previous paper was where there is uncertainty about the number of parameters needed to specify a model. This arises because there may be uncertainty about the number of terms to be included in the regression model to be fitted. The statistically non-standard nature of the problem means that it requires special handling. In this paper, the author uses the derived chain method suggested in the previous paper. However, whereas in that paper the distribution of the response output of interest was assumed to be simply normal, it is typically the case, especially in the study of systems working near their capacity limit, that this distribution is skewed, and moreover the distribution has a support that is effectively bounded from below-i.e. the distribution has a threshold. We describe how the derived MCMC method might be applied in this situation and illustrate it with a numerical example involving the simulation of a computer PAD network.