Gearing Gaussian process modeling and sequential design towards stochastic simulators

TL;DR

This paper explores advanced Gaussian process modeling techniques for complex noise in stochastic simulators, comparing various approaches and adapting sequential design methods, demonstrated through an epidemiology example.

Contribution

It provides a comprehensive review and comparison of Gaussian process models with complex noise handling and introduces adapted sequential design procedures for stochastic simulators.

Findings

Comparison of noise modeling approaches in Gaussian processes

Adaptation of sequential design for complex noise scenarios

Application to an epidemiology case study

Abstract

This chapter presents specific aspects of Gaussian process modeling in the presence of complex noise. Starting from the standard homoscedastic model, various generalizations from the literature are presented: input varying noise variance, non-Gaussian noise, or quantile modeling. These approaches are compared in terms of goal, data availability and inference procedure. A distinction is made between methods depending on their handling of repeated observations at the same location, also called replication. The chapter concludes with the corresponding adaptations of the sequential design procedures. These are illustrated in an example from epidemiology.