Diagnostic-Driven Nonstationary Emulators Using Kernel Mixtures

TL;DR

This paper presents a diagnostic-driven method for fitting nonstationary Gaussian process emulators by using mixtures of region-specific kernels, improving predictive performance in nonstationary settings.

Contribution

It introduces a novel approach that combines diagnostics with kernel mixtures to model nonstationarity in Gaussian process emulators, enhancing interpretability and continuity.

Findings

The method effectively captures nonstationarity in test cases.

It outperforms traditional stationary GP models in nonstationary scenarios.

Application to climate modeling demonstrates practical utility.

Abstract

Weakly stationary Gaussian processes (GPs) are the principal tool in the statistical approaches to the design and analysis of computer experiments (or Uncertainty Quantification). Such processes are fitted to computer model output using a set of training runs to learn the parameters of the process covariance kernel. The stationarity assumption is often adequate, yet can lead to poor predictive performance when the model response exhibits nonstationarity, for example, if its smoothness varies across the input space. In this paper, we introduce a diagnostic-led approach to fitting nonstationary GP emulators by specifying finite mixtures of region-specific covariance kernels. Our method first fits a stationary GP and, if traditional diagnostics exhibit nonstationarity, those diagnostics are used to fit appropriate mixing functions for a covariance kernel mixture designed to capture the nonstationarity, ensuring an emulator that is continuous in parameter space and readily interpretable. We compare our approach to the principal nonstationary GP models in the literature and illustrate its performance on a number of idealised test cases and in an application to modelling the cloud parameterization of the French climate model.