Statistical analysis of multivariate computer output

Abstract

Many scientific investigations rely on computer models for simulating plausible real situations. In trying to describe the complexities of reality, some computer models are themselves very complex and are therefore expensive to run. In response to some of these issues, a recent approach proposes to use statistical models as less computationally demanding surrogates of such complex computer models. The statistical surrogates do not exactly match the computer model output in a new situation, but these have the capability to describe the associated uncertainty. Ideally, the completed statistical model would not require as many computational resources as the original computer model. Chapter 1 surveys briefly the literature related to the statistical analysis of computer experiments. While most applications implementing the above statistical methodology deal with scalar output, this dissertation suggests methodologies for analyzing multivariate computer output. In particular, Chapter 2 implements a method for the statistical analysis of time series produced by finite difference solvers of differential equations. This statistical model makes use of the underlying code information and, as a result, is second-order non-stationary. The Lotka-Volterra competing species differential system is used as an example to illustrate the methods. It is shown that the statistical model proposed here is more accurate than a statistical model that extends directly the existing scalar methodology to the multivariate case. However, the method is useful only in cases where the output can be easily saved and manipulated numerically. Chapter 3 suggests a two-stage method for the analysis of multivariate computer output in cases when at least one dimension is large, in particular when the number of temporal points is large. A double-gyre ocean system of partial differential equations is used to illustrate this method. Chapter 4 outlines preliminary work on two additional methodologies concerning the statistical analysis of multivariate computer output.