# Diagnostic-Driven Nonstationary Emulators Using Kernel Mixtures

arXiv: https://arxiv.org/abs/1803.04906 · HTML: https://mlsanity.com/paper/1803.04906/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Mar 2018.

## Built on by (most cited first, 4 of 4)

- [Deep Gaussian Process Emulation using Stochastic Imputation](https://mlsanity.com/paper/2107.01590/) (2021)
- [On MCMC for variationally sparse Gaussian processes: A pseudo-marginal approach](https://mlsanity.com/paper/2103.03321/) (2021)
- [Linked Deep Gaussian Process Emulation for Model Networks](https://mlsanity.com/paper/2306.01212/) (2023)
- [DeRegiME: Deep Regime Mixtures for Probabilistic Forecasting under Distribution Shift](https://mlsanity.com/paper/2605.19231/) (2026)

## Abstract (arXiv)

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.