Bayesian Decision Theory

In this chapter we shall present a review of decision theory based on the Bayesian approach to statistical inference and decision making. Decision theory deals with the development of methods and techniques that are appropriate for making decisions in an optimal fashion. In fact, statistics itself is sometimes described as the science of decision making under uncertainty. Although decision theory may not encompass the entire field of statistics, the importance of decision theory has steadily grown during the past 30 years as virtually all the classical problems of statistical inference, and many new problems as well, have been formulated in decision-theoretic terms.