ABSTRACT
Most of this book has been concerned with the so-called frequentist approach to
inference, which is based on the concept of repeated sampling and the relative fre-
quency interpretation of probability. At a couple of points we have referred to the
existence of a completely different approach, called the Bayesian approach. In one
chapter we do not have enough space to give a full treatment of Bayesian inference,
but given its growing importance in modern statistical practice we provide here an
introduction. Our aim is to provide a grounding in the basic concepts of Bayesian
statistics, supplemented by some simple illustrations based on our earlier examples
and exercises. We first give a brief overview of how the Bayesian approach differs
from the frequentist approach, including the subjective interpretation of probability,
and then provide some basic technical details relating to Bayes’ rule. Next we intro-
duce the important Bayesian concepts of prior and posterior distributions, as well as
the Bayesian counterpart of confidence intervals, credible intervals. The connection
between Bayesian and likelihood inference is then reviewed, followed by a Bayesian
re-examination of the treatment comparison example discussed in Chapter 5.
