Enhancing Response Predictions with a Joint Gaussian Process Model for Stochastic Simulation Models

The stochastic Gaussian process model has been widely used in stochastic simulation metamodeling. In practice, the performance of this model can be largely affected by the noise in the observations. In this article, we propose an approach to mitigate the impact of the noisy observations by jointly modeling the response of interest with a correlated but less-noisy auxiliary response. The main idea is to leverage on and learn from the correlated and more accurate response to improve the prediction. To achieve this, we extend the existing deterministic multi-response model for stochastic simulation to jointly model the two responses, use some simplified examples to show the benefit of the proposed model, and investigate the input estimation of this model. Quantile prediction is used to illustrate the efficiency of the proposed approach by jointly modeling it with the expectation, which typically has a less noisy estimator compared with that of the quantile. Several numerical examples are then conducted, and the results show that the joint model can provide better performance. These promising results illustrate the potential of this joint model especially in situations where the response of interest is much noisier or when observations are scarce. We further propose a two-stage design approach based on the multi-response model to more efficiently utilize limited computing budget to improve predictions. We also see from these designs the benefits of the joint model, where the more accurate auxiliary response observations can be used to improve the response of interest.