Optimal static and sequential design : a critical review

Ford, Ian (1976) Optimal static and sequential design : a critical review. PhD thesis, University of Glasgow.

Abstract

The aim of this thesis is to review and augment the theory and
methods of optimal experimental design.
In Chapter I the scene is set by considering the possible aims
of an experimenter prior to an experiment, the statistical methods
one might use to achieve those aims and how experimental design
might aid this procedure. It is indicated that, given a criterion
for design, a priori optimal design will only be possible in certain
instances and, otherwise, some form of sequential procedure would seem
to be indicated.
In Chapter 2 an exact experimental design problem is formulated
mathematically and is compared with its continuous analogue.
Motivation is provided for the solution of this continuous problem,
and the remainder of the chapter concerns this problem. A
necessary and sufficient condition for optimality of a design measure
is given. Problems which might arise in testing this condition are
discussed, in particular with respect to possible non-differentiability
of the criterion function at the design being tested. Several
examples are given of optimal designs which may be found analytically
and which illustrate the points discussed earlier in the chapter.

In Chapter 3 numerical methods of solution of the continuous
optimal design problem are reviewed. A new algorithm is presented
with illustrations of how it should be used in practice. It is shown
that, for reasonably large sample size, continuously optimal designs
may be approximated to well by an exact design. In situations
where this is not satisfactory algorithms for improvement of this
design are reviewed.
Chapter 4 consists of a discussion of sequentially designed
experiments, with regard to both the philosophies underlying, and the
application of the methods of, statistical inference.
In Chapter 5 we criticise constructively previous suggestions
for fully sequential design procedures. Alternative suggestions are
made along with conjectures as to how these might improve performance.
Chapter 6 presents a simulation study, the aim of which is to
investigate the conjectures of Chapter 5. The results of this study
provide empirical support for these conjectures.
In Chapter 7 examples are analysed. These suggest aids to sequential experimentation by means of reduction of the dimension of the design space and the possibility of experimenting semi-sequentially.
Further examples are considered which stress the importance of the
use of prior information in situations of this type. Finally we
consider the design of experiments when semi-sequential experimentation
is mandatory because of the necessity of taking batches of observations
at the same time.
In Chapter 8 we look at some of the assumptions which have been
made and indicate what may go wrong where these assumptions no longer
hold.

• Item Type: Thesis (PhD)
• Qualification Level: Doctoral
• Subjects: H Social Sciences > HA Statistics
• Colleges/Schools: College of Science and Engineering > School of Mathematics and Statistics > Statistics
• Supervisor's Name: Silvey, Professor S. D.
• Date of Award: 1976
• Depositing User: Adam Swann
• Unique ID: glathesis:1976-7556
• Copyright: Copyright of this thesis is held by the author.
• Date Deposited: 07 Sep 2016 10:10
• Last Modified: 07 Sep 2016 10:10
• URI: https://theses.gla.ac.uk/id/eprint/7556