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Statistical decision theory and Bayesian analysis are related at a number of levels. First, they are both needed to solve real decision problems, each embodying a description of one of the key elements of a decision problem. At a deeper level, Bayesian analysis and decision theory provide unified outlooks towards statistics they give a foundational framework for thinking about statistics and for evaluating proposed statistical methods.
The relationships (both conceptual and mathematical) between Bayesian analysis and statistical decision theory are so strong that it is somewhat unnatural to learn one without the other. Nevertheless, major portions of each have developed separately. On the Bayesian side, there is an extensively developed Bayesian theory of statistical inference (both subjective and objective versions). This theory recognizes the importance of viewing statistical analysis conditionally (i.e., treating observed data as known rather than unknown), even when no loss function is to be incorporated into the analysis. There is also a well-developed (frequentist) decision theory, which avoids formal utilization of prior distributions and seeks to provide a foundation for frequentist statistical theory. Although the central thread of the book will be Bayesian decision theory, both Bayesian inference and non-Bayesian decision theory will be extensively discussed. Indeed, the book is written so as to allow, say, the teaching of a course on either subject separately.
Basic concepts.
Utility and loss.
Prior information and subjective probability.
Bayesian analysis.
Minimax analysis.
Invariance.
Preposterior and sequential analysis.
Complete and essentially complete classes.
Appendices