ABSTRACT
The prior distribution plays a defining role in Bayesian analysis. In view of the controversy surrounding its use it may be tempting to treat it almost as an embarrassment and to emphasise its lack of importance in particular applications, but we feel it is a vital ingredient and needs to be squarely addressed. In this chapter we introduce basic ideas by focusing on single parameters, and in subsequent chapters consider multi-parameter situations and hierarchical models. Our emphasis is on understanding what is being used and being aware of its (possibly unintentional) influence.
