1 - Conditioning and Likelihood.- What Is the Likelihood Function?.- Discussion.- Discussion.- Reply to Discussion.- The Relevance of Stopping Rules in Statistical Inference.- Discussion.- Discussion.- Discussion.- Reply to Discussion.- Conditionally Acceptable Frequentist Solutions.- Discussion.- Discussion.- Discussion.- Discussion.- Discussion.- Reply to Discussion.- On the Validity of the Likelihood Principle.- Resampling Generated Likelihoods.- 2 - Bayes and Empirical Bayes Analysis.- Bayesian Linear Probabilistic Classification.- Bayesian Numerical Analysis.- Estimating Logistic Regression Probabilities.- Bayes and Empirical Bayes Analysis in Multistage Sampling.- Empirical Bayes Rules for Selecting the Best Binomial Population.- A Bayesian Treatment of Multivariate Normal Data with Observations Missing at Random.- Causality Assessment for Adverse Drug Reactions: An Application of Subjective Probability to Medical Decision Making.- Determining the Accuracy of Bayesian Empirical Bayes Estimates in the Familiar Exponential Families.- The U,V Method of Estimation.- Some Results on Robustness in Testing.- 3 - Decision-Theoretic Estimation.- Shrinkage Estimators: Pseudo-Bayes Rules for Normal Mean Vectors.- The Differential Inequality of a Statistical Estimation Problem.- Bayesian Estimation Subject to Minimaxity of the Mean of a Multivariate Normal Distribution in the Case of a Common Unknown Variance: A Case for Bayesian Robustness.- New Estimators for the Mean Vector of a Normal Distribution with Unknown Covariance Matrix.- On Inadmissibility of Some Unbiased Estimates of Loss.- Dominating Inadmissible Procedures Using Compromise Decision Theory.- On Estimating Characteristic Roots in a Two-Sample Problem.- On Admissible Estimation in Exponential Families with Imprecise Information.- Estimated Loss and Admissible Loss Estimators.
The Fourth Purdue Symposium on Statistical Decision Theory and Related Topics was held at Purdue University during the period June 15-20, 1986. The symposium brought together many prominent leaders and younger researchers in statistical decision theory and related areas. The 65 invited papers and discussions presented at the symposium are collected in this two-volume work. The papers are grouped into a total of seven parts. Volume I has three parts: Part 1 -Conditioning and Likelihood; Part f! - Bayes and Empirical Bayes Analysis; and Part 9 -Decision Theoretic Estimation. Part 1 contains the proceedings of a Workshop on Conditioning, which was held during the symposium. Most of the articles in Volume I involve either conditioning or Bayesian ideas, resulting in a volume of considerable interest to conditionalists and Bayesians as well as to decision-theorists. Volume II has four parts: Part 1 -Selection, Ranking, and Multiple Com parisons; fart f! -Asymptotic and Sequential Analysis; Part 9 -Estimation and Testing; and Part -4 -Design and Comparison of Experiments and Distributions. These articles encompass the leading edge of much current research in math ematical statistics, with decision theory, of course, receiving special emphasis. It should be noted that the papers in these two volumes are by no means all theoretical; many are applied in nature or are creative review papers.
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