Applied statistical decision theory

In the field of statistical decision theory, Raiffa and Schlaifer have sought to develop new analytic techniques by which the modern theory of utility and subjective probability can actually be applied to the economic analysis of typical sampling problems. —From the foreword to their classic work Applied Statistical Decision Theory . First published in the 1960s through Harvard University and MIT Press, the book is now offered in a new paperback edition from Wiley Booknews Addressed to those who are interested in using statistics as a tool in practical problems of decision making under conditions of uncertainty and who also have the necessary training in mathematics and statistics to employ these analytical techniques. The underlying principle of the material outlined in the book is the Bayesian approach which provides a formal mechanism for taking account of preferences and weights rather than leaving it up to the decision maker's intuition. Topics covered include sufficient statistics and noninformative stopping, conjugate prior distributions, additive utility and opportunity loss, linear terminal analysis, selection of processes, problems in which the act and state spaces coincide, multivariate normalized density functions, Bernoulli process, Poisson process, independent normal process, and normal regression process. Annotation c. Book News, Inc., Portland, OR (booknews.com) Content: Part I Experimentation and Decision: General Theory -- 1. Problem and the Two Basic Modes of Analysis 3 -- 1. Description of the Decision Problem -- 2. Analysis in Extensive Form -- 3. Analysis in Normal Form -- 4. Combination of Formal and Informal Analysis -- 5. Prior Weights and Consistent Behavior -- 2. Sufficient Statistics and Noninformative Stopping 28 -- 2. Sufficiency -- 3. Noninformative Stopping -- 3. Conjugate Prior Distributions 43 -- 2. Conjugate Prior Distributions -- 3. Choice and Interpretation of a Prior Distribution -- 4. Analysis in Extensive Form when the Prior Distribution and Sample Likelihood are Conjugate -- Part II Extensive-Form Analysis When Sampling and Terminal Utilities Are Additive -- 4. Additive Utility, Opportunity Loss, and the Value of Information: Introduction to Part II 79 -- 1. Basic Assumptions -- 2. Applicability of Additive Utilities -- 3. Computation of Expected Utility -- 4. Opportunity Loss -- 5. Value of Information -- 5A. Linear Terminal Analysis 93 -- 2. Expected Value of Perfect Information when [omega] is Scalar -- 3. Preposterior Analysis -- 4. Prior Distribution of the Posterior Mean [omega]" for Given e -- 5. Optimal Sample Size in Two-Action Problems when the Sample Observations are Normal and Their Variance is Known -- 6. Optimal Sample Size in Two-Action Problems when the Sample Observations are Binomial -- 5B. Selection of the Best of Several Processes 139 -- 8. Analysis in Terms of Differential Utility -- 9. Distribution of [delta] and [delta]" when the Processes are Independent Normal and [upsilon] is Linear in [mu] -- 10. Value of Information and Optimal Size when There are Two Independent Normal Processes -- 11. Value of Information when There are Three Independent-Normal Processes -- 12. Value of Information when There are More than Three Independent-Normal Processes -- 6. Problems in Which the Act and State Spaces Coincide 176 -- 2. Certainty Equivalents and Point Estimation -- 3. Quadratic Terminal Opportunity Loss -- 4. Linear Terminal Opportunity Loss -- 5. Modified Linear and Quadratic Loss Structures -- Part III Distribution Theory -- 7. Univariate Normalized Mass and Density Functions 211 -- A. Natural Univariate Mass and Density Functions 213 -- 1. Binomial Function -- 2. Pascal Function -- 3. Beta Functions -- 4. Inverted Beta Functions -- 5. Poisson Function -- 6. Gamma Functions -- 7. Inverted Gamma Functions -- 8. Normal Functions -- B. Compound Univariate Mass and Density Functions 232 -- 9. Student Functions -- 10. Negative-Binomial Function -- 11. Beta-Binomial and Beta-Pascal Functions -- 8. Multivariate Normalized Density Functions 242 -- 1. Unit-Spherical Normal Function -- 2. General Normal Function -- 3. Student Function -- 4. Inverted-Student Function -- 9. Bernoulli Process 261 -- 1. Prior and Posterior Analysis -- 2. Sampling Distributions and Preposterior Analysis: Binomial Sampling -- 3. Sampling Distributions and Preposterior Analysis: Pascal Sampling -- 10. Poisson Process 275 -- 1. Prior and Posterior Analysis -- 2. Sampling Distributions and Preposterior Analysis: Gamma Sampling -- 3. Sampling Distributions and Preposterior Analysis: Poisson Sampling -- 11. Independent Normal Process 290 -- A. Mean Known 290 -- 1. Prior and Posterior Analysis -- 2. Sampling Distributions and Preposterior Analysis with Fixed v -- B. Precision Known 294 -- 3. Prior and Posterior Analysis -- 4. Sampling Distributions and Preposterior Analysis with Fixed n -- C. Neither Parameter Known 298 -- 5. Prior and Posterior Analysis -- 6. Sampling Distributions with Fixed n -- 7. Preposterior Analysis with Fixed n -- 12. Independent Multinormal Process 310 -- A. Precision Known 310 -- 1. Prior and Posterior Analysis -- 2. Sampling Distributions with Fixed n -- 3. Preposterior Analysis with Fixed n -- B. Relative Precision Known 316 -- 4. Prior and Posterior Analysis -- 5. Sampling Distributions with Fixed n -- 6. Preposterior Analysis with Fixed n -- C. Interrelated Univariate Normal Processes 326 -- 8. Analysis When All Processes Are Sampled -- 9. Analysis when Only p < r Processes are Sampled -- 13. Normal Regression Process 334 -- A. Precision Known 336 -- 2. Prior and Posterior Analysis -- 3. Sampling Distributions with Fixed X -- 4. Preposterior Analysis with Fixed X of Rank r -- B. Precision Unknown 342 -- 5. Prior and Posterior Analysis -- 6. Sampling Distributions with Fixed X -- 7. Preposterior Analysis with Fixed X of Rank r -- C. X[superscript t] X Singular 349 -- 9. Distributions of b* and v -- 10. Preposterior Analysis.