Statistical Decision Theory: Concepts, Methods and Applications (Special topics in Probabilistic Graphical Models) FIRST COMPLETE DRAFT November 30, 2003 Supervisor: Professor J. Rosenthal STA4000Y Anjali Mazumder 950116380
Part I: Decision Theory – Concepts and Methods 1
Part I: DECISION THEORY - Concepts and Methods Decision theory as the name would imply is concerned with the process of making decisions. The extension to statistical decision theory includes decision making in the presence of statistical knowledge which provides some information where there is uncertainty. The elements of decision theory are quite logical and even perhaps intuitive. The classical approach to decision theory facilitates the use of sample information in making inferences about the unknown quantities. Other relevant information includes that of the possible consequences which is quantified by loss and the prior information which arises from statistical investigation. The use of Bayesian analysis in statistical decision theory is natural. Their unification provides a foundational framework for building and solving decision problems. The basic ideas of decision theory and of decision theoretic methods lend themselves to a variety of applications and computational and analytic advances. This initial part of the report introduces the basic elements in (statistical) decision theory and reviews some of the basic concepts of both frequentist statistics and Bayesian analysis. This provides a foundational framework for developing the structure of decision problems. The second section presents the main concepts and key methods involved in decision theory. The last section of Part I extends this to statistical decision theory – that is, decision problems with some statistical knowledge about the unknown quantities. This provides a comprehensive overview of the decision theoretic framework.