Prediction of non-stationary response functions using a Bayesian composite Gaussian process

The modeling and prediction of functions that can exhibit non-stationarity characteristics is important in many applications; for example, this often the case simulator output. One approach to predict a function with unknown stationarity properties model it as draw from flexible stochastic process produce stationary or non-stationary realizations. such composite Gaussian (CGP) which expresses large-scale (global) trends output small-scale (local) adjustments global trend independent processes; an extension CGP realizations non-constant variance by allowing local vary over input space. A new, Bayesian global-trend plus local-trend proposed also allows measurement errors. In contrast original model, new introduces weight allow total variability be apportioned between large- processes. prior distributions ensure fitted mean smoother than deviations, feature built into model. log modeled provide mechanism handling across Markov chain Monte Carlo algorithm provides posterior estimates parameters CGP. It yields predictions quantifies uncertainty about predictions. method illustrated using both analytic real-data examples.