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UBC Theses and Dissertations

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UBC Theses and Dissertations

Designs for computer experiments : random versus rational Gustafsson, Emelie Anna

Abstract

Computer experiments facilitate, through mathematical modelling, various experiments that would otherwise be very difficult to perform, or even impossible. Computer experiments are employed to emulate situations in areas such as weather modelling, astrophysics, economics and many more. In conducting a computer experiment, we are required to select a design for the initial values x⁽¹⁾, . . . , x(n) of a process, and then emulate the output based on the process and the initial values. The quality of the emulator therefore depends partly on the process and partly on the choice of initial values. We will only consider the Gaussian Process in this thesis, and the focus of our analysis will be on the selection of initial values. We consider the effects of selecting a random versus a rational design for the initial values of computer experiments. We aim to study a broad range of possible computer models that are likely to arise in practice. Therefore, we present the analysis of eight different design choices, each of which is either random or rational, for the initial values. These initial values are applied to five different test functions that we consider to be prevalent in practice. We observe the effect of each of the designs on each of the test functions at three different sample sizes. The goal of this thesis is to present a comprehensive study of various standard design choices and make recommendations to a practitioner on a robust design for the initial values of a computer experiment on a given function. As well as ultimately recommend a universally robust design for the initial values of any computer experiment.

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