Fully Bayesian Sequential Design for Mean Response Surface Prediction of Heteroscedastic Stochastic Simulations

We present a fully Bayesian sequential strategy for predicting the mean response surface of heteroscedastic stochastic simulation functions. Leveraging dual Gaussian processes as the surrogate model and a criterion based on empirical expected integrated mean-square prediction error, our approach sequentially selects informative design points while fully accounting for parameter uncertainty. Sequential importance sampling is employed to efficiently update the posterior distribution of the parameters. Our strategy is tailored for expensive simulation functions, where achieving robust predictive accuracy under a limited budget is critical. We illustrate its potential advantages compared to existing approaches through synthetic examples. We then implement the proposed strategy on a real motivating application in seismic design of wood-frame podium buildings.