A Bayesian metamodeling approach for stochastic simulations

Abstract

In the application of kriging model in the field of simulation, the parameters of the model are likely to be estimated from the simulated data. This introduces parameter estimation uncertainties into the overall prediction error, and this uncertainty can be further aggravated by random noise in the stochastic simulation. In this paper, a Bayesian metamodeling approach for kriging prediction is proposed for stochastic simulations to more appropriately account for the parameter uncertainties. The approach is first illustrated analytically using a simplified two point example. A more general Markov Chain Monte Carlo analysis approach is subsequently proposed to handle more general assumptions on the parameters and design. The general MCMC approach is compared with the modified nugget effect kriging model based on the M/M/1 simulation system. Initial results indicate that the Bayesian approach has better coverage and closer predictive variance to the empirical value than the modified nugget effect kriging model, especially in the cases where the stochastic variability is high.