Applied statistical decision theory

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.