Bayesian Approaches to Clinical Trials and Health-Care Evaluation
Chapter One
Introduction
1.1 WHAT ARE BAYESIAN METHODS?
Bayesian statistics began with a posthumous publication in 1763 by Thomas
Bayes, a Nonconformist minister from the small English town of Tunbridge Wells.
His work was formalised as Bayes theorem which, when expressed mathematically,
is a simple and uncontroversial result in probability theory. However,
specific uses of the theorem have been the subject of continued controversy for
over a century, giving rise to a steady stream of polemical arguments in a number
of disciplines. In recent years a more balanced and pragmatic perspective has
developed and this more ecumenical attitude is reflected in the approach taken in
this book: we emphasise the benefits of Bayesian analysis and spend little time
criticising more traditional statistical methods.
The basic idea of Bayesian analysis is reasonably straightforward. Suppose an
unknown quantity of interest is the median years of survival gained by using an
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