Statistical Modelling and Analysis of the Computer-Simulated Datasets

TL;DR

This paper reviews statistical modeling techniques for analyzing data from computer simulators, highlighting Gaussian Process models, their challenges, and recent generalizations for big data analysis in simulation experiments.

Contribution

It provides a comprehensive review of Gaussian Process models, discusses numerical stability issues, and introduces recent generalizations for analyzing large-scale computer simulation data.

Findings

Gaussian Process models are widely used for surrogate modeling.

Numerical instability due to near-singularity affects GP fitting.

Recent methods improve analysis of large-scale simulation data.

Abstract

Over the last two decades, the science has come a long way from relying on only physical experiments and observations to experimentation using computer simulators. This chapter focusses on the modelling and analysis of data arising from computer simulators. It turns out that traditional statistical metamodels are often not very useful for analyzing such datasets. For deterministic computer simulators, the realizations of Gaussian Process (GP) models are commonly used for fitting a surrogate statistical metamodel of the simulator output. The chapter starts with a quick review of the standard GP based statistical surrogate model. The chapter also emphasizes on the numerical instability due to near-singularity of the spatial correlation structure in the GP model fitting process. The authors also present a few generalizations of the GP model, reviews methods and algorithms specifically developed for analyzing big data obtained from computer model runs, and reviews the popular analysis goals of such computer experiments. A few real-life computer simulators are also briefly outlined here.