Multivariate Stochastic Process Models for Correlated Responses of Mixed Type

We propose a new model for correlated outputs of mixed type, such as continuous and binary outputs, with a particular focus on joint regression and classification, motivated by an application in constrained optimization for com- puter simulation modeling. Our framework is based upon multivariate stochastic processes, extending Gaussian process methodology for modeling of continuous multivariate spatial outputs by adding a latent process structure that allows for joint modeling of a variety of types of correlated outputs. In addition, we imple- ment fully Bayesian inference using particle learning, which allows us to conduct fast sequential inference. We demonstrate the effectiveness of our proposed meth- ods on both synthetic examples and a real world hydrology computer experiment optimization problem where it is helpful to model the black box objective function as correlated with satisfaction of the constraint.