Bayesian Statistical Analysis
David Spiegelhalter, MRC Biostatistics Unit, Institute for Public Health,
Cambridge
The first part of the tutorial will cover the fundamentals of Bayesian
inference, including probability and its subjective interpretation,
evaluation of probability assessments using scoring rules, utilities
and decision theory. The use of Bayes theorem for updating beliefs
will be illustrated for both binomial and normal likelihoods, and the
use of conjugate families of priors and predictive distributions
described. The First Bayes software will be used to display conjugate
Bayesian analysis.
The second part will introduce the concept of `exchangeability', and
the consequent use of hierarchical models in which the unknown
parameters of a common prior are included in the model. Conditional
independence assumptions lead naturally to a graphical representation
of hierarchical models. Markov chain Monte Carlo (MCMC) methods will
be introduced as a means of carrying out the necessary numerical
integrations, and topics covered will include the relationship of
Gibbs sampling to graphical modelling, parameterisation, initial
values, and choice of prior distributions. Real examples will be used
throughout, and on-line analysis of an example in longitudinal
modelling with measurement error on predictors will be carried out
using the WinBUGS program.