PHARMACEUTICAL STATISTICSPharmaceut. Statist. 2008; 7: 305–307

Published online in Wiley InterScience (www.interscience.wiley.com).

Book Reviews

Understanding Uncertainty

Lindley D (2006)

ISBN: 0470043830; 250 pages; £34.50, h48.90, $64.95

Wiley; http://www.wiley.com/

This book is intended for the general reader, and it does not

require much previous experience of statistics. The author

writes it towards the end of a long and distinguished career, in

an attempt to communicate and summarize his views on the

subject – central not only to our own discipline but also to

many areas of science and more generally in society. I

recommend it as a well-written and authoritative source of

information about many of the basic issues that underlie

problems we face regularly, and particularly about the Bayesian

philosophy that the author has long championed.

Between the personal statements in the Prologue and

Epilogue, the book has three parts, as I see it. The first two

chapters, ‘Uncertainty’ and ‘Stylistic Questions’, introduce the

subject and the context in which these issues are relevant. The

central part of the book is an attempt to develop probability

theory in a non-specialist way. After laying out the basic ideas

of probability, the author starts with two events and looks at

the rules of probability, particularly Bayes’ Rule. Then there is

an important digression on ‘Measuring uncertainty’, before

moving on to the theory for three events, and then more

generally to a chapter on variation, which describes distribu-

tions. The third part, after first looking at the methodology of

decision analysis, branches out to look at the way the scientific

method works with uncertainty, and then goes through seven

examples that many readers will have come across before,

before concluding with a chapter on ‘Probability Assessment’.

I find the central part mostly rather pointless. Of course, it is

not intended for statisticians like myself who have learnt about

and used probability since school days and have been

introduced to the idea of drawing balls from urns. However, I

feel that the stated aim of introducing these arguments to a lay

audience is expecting far more than reasonable from people not

used to mathematics, even though equations with Greek

characters are kept to a minimum. However, it would be more

appropriate for this aspect to be judged by non-statisticians –

suffice it to say that most of this part can be readily skipped by

statisticians unless they want to refresh the grounding of their

subject. There are excellent sections within it, however,

particularly the explanation of Simpson’s paradox in Chapter

8. Chapter 7 deals with the essential issue of how to go about

measuring uncertainty, which is one of the main stumbling

blocks for the Bayesian approach from my point of view as a

frequentist by training and practice. This issue appears early in

Chapter 3 when discussing how to measure the intensity of

belief: ‘Many people object to the assignment of numbers’.

Despite reading most of the book, including the final chapter on

probability assessment, I still find this a big problem. The

Bayesian method needs this assignment, and methods are

proposed for achieving it, but I am uncomfortable with

grounding my subsequent inference on what feels to me to be

mostly guesswork. One of the crucial arguments is in Section

3.4, where the fact of holding opposing beliefs at either end of a

scale of values is taken to imply that there ‘must be an

intermediate value’ where the beliefs are held equally.

The final part is well worth dipping into, particularly the

clear exposition of the examples of using probability arguments

to handle awkward questions like those about UFOs and well-

known game-show problems.

When it comes to the pharmaceutical industry, there are clear

messages about the potential use of rational probability

arguments in drug development, and I am sure that these

should be brought to bear more on the general processes within

companies and institutions. However, when it comes to the later

stages of development, the statement on Page 10 is very telling:

‘We develop a calculus for ‘you’; there does not exist an entirely

satisfactory calculus for two or more competitors and, in my

view, this omission presents a serious, unsolved problem’.

Hence, the idea of a pharmaceutical company using a fully

Bayesian approach in confirmatory trials that are to be judged

by regulators is not one that is likely to catch on.

Peter Lane

Research Statistics Unit, GlaxoSmithKline

(DOI: 10.1002/pst.330)

Copyright # 2008 John Wiley & Sons, Ltd.Received 15 January 20012008