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 computer 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 implement fully Bayesian inference using particle learning, which allows us to conduct fast sequential inference. We demonstrate the effectiveness of our proposed methods 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.