The Design and Analysis of Computer Experiments (Springer Series in Statistics)

The Design and Analysis of Computer Experiments (Springer Series in Statistics)

By Thomas J. Santner, Brian J. Williams, William Notz,

Publisher: Springer
Number Of Pages: 283
Publication Date: 2003-07-30
Sales Rank: 556014
ISBN / ASIN: 0387954201
EAN: 9780387954202
Binding: Hardcover
Manufacturer: Springer
Studio: Springer
Average Rating: 4

In the past 15 to 20 years, the computer has become a popular tool for exploring the relationship between a measured response and factors thought to affect the response. In many cases, scientific theories exist that implicitly relate the response to the factors by means of systems of mathematical equations. There also exist numerical methods for accurately solving such equations and appropriate computer hardware and software to implement these methods. In many engineering applications, for example, the relationship is described by a dynamical system and the numerical method is a finite element code. In such situations, these numerical methods allow one to produce computer code that can generate the response corresponding to any given set of values of the factors. This allows one to conduct an "experiment" (called a "computer experiment") to explore the relationship between the response and the factors using the code. Indeed, in some cases computer experimentation is feasible when a properly designed physical experiment (the gold standard for establishing cause and effect) is impossible. For example, the number of input variables may be too large to consider performing a physical experiment or it may simply be economically prohibitive to run an experiment on the scale required to gather sufficient information to answer a particular research question. This book describes methods for designing and analyzing experiments conducted using computer code in lieu of a physical experiment. It discusses how to select the values of the factors at which to run the code (the design of the computer experiment) in light of the research objectives of the experimenter. It also provides techniques for analyzing the resulting data so as to achieve these research goals. It illustrates these methods with code that is available to the reader at

Review:

A valuable description of core material in the field of computer experiments

This is a description of core practice in computer experiments,
written by authorities in the field. After an introduction it divides
into three parts: (1) building a statistical model of the underlying
computer code, known as a surrogate or an emulator; (2) choosing at
which settings to evaluate the code, eg, for the purposes of building
an emulator or for optimisation; (3) inference and validation (a
single chapter). There is a brief Appendix containing basic
distributional information, and a more extensive Appendix describing
the PErK software for building an emulator.

This book is consistent in its level and presentation. It serves as
an introduction to the field, providing orientation and an overview of
the literature. It is moderately technical; a Masters Statistician
should be comfortable with the mathematics. Derivations, where they
are given, are thorough, and the key results are clearly (sometimes
exhaustively!) presented. The technical and practical material is
well-blended. The Ch 2 material on stochastic processes gives a good
example of this: the boundary between what needs to be known and what
can be taken as given is well-delineated, and references are given by
author and page.

Note, however, that this book does not claim to be a handbook to
performing computer experiments: as far as I know such a book does not
exist. There are technical issues which the book does not address but
which are important in practice. In particular, choice of regression
functions and empirical estimation of correlation lengths in the
residual process---as advocated by the authors---can be very tricky in
practice. For this reason, I would like to have seen material on
emulator diagnostics: leave-one-out, or one-step-ahead (prequential),
for example.

As a broader observation, the authors' treatment seems tuned mainly to
engineering applications. Many computer experiments concern
environmental applications, which introduce a number of additional
challenges. Issues of scale are often a practical problem: how to
deal with large input spaces, large output spaces, and long
model-evaluation times. The uncertain model-inputs, for example,
might include the initial value of the state vector and the forcing,
comprising thousands of quantities if we are dealing with a climate
model. This will affect both emulator construction and experimental
design (sequential experimental design becomes much more important).
For environmental models the issue of model-validation can be subtle,
requiring as it does our assessment of model-imperfections: these can
be the dominant source of uncertainty, unlike in many engineering
applications.

This is not to criticise the authors, whose book which is usually on
or near my desk. They have done an excellent job of describing the
core material in a rapidly-developing field.

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