The chapters in this section describe an approach to inferential statistics that differs in several fundamental ways from what is usually taught in introductory courses. The standard approach is often referred to as sampling theory inference because of its em& phasis on the behavior of repeated (hypothetical) samples similar to the one actually obtained. It forms the basis for most of the statistically oriented chapters in this book.
Bayesian inference, on the other hand, makes no reference to repeated sampling. Instead, it provides a framework for making direct probability statements about unknown parameters, such as population means, based on the data at hand as well as any pre& viously available information. The origin of this approach is asso& ciated with the eighteenth century mathematician Thomas Bayes, whose theorem regarding conditional probabilities forms the basis of its primary inferential mechanism. Nevertheless, most of the important developments in Bayesian statistics have been relatively recent.
Chapter 7, by Winkler, introduces several forms of Bayes' Theorem, working with probabilities for single events, as well as discrete and continuous random variables. The author then dis& cusses issues associated with expressing prior knowledge and in& formation contained in the sample data in a form that facilitates the application of Bayes' Theorem. Bayesian approaches to prob& lems in estimation, hypothesis testing, prediction and decision