Introduction To Statistical Decision Theory

According to the authors, the Bayesian revolution in statistics - where statistics is integrated with decision making in areas such as management, public policy, engineering, and clinical medicine - is here to stay. "Introduction to Statistical Decision Theory" states the case and in a self-contained, comprehensive way shows how the approach is operational and relevant for real-world decision making under uncertainty. Starting with an extensive account of the foundations of decision theory, the authors develop the intertwining concepts of subjective probability and utility. They then systematically and comprehensively examine the Bernoulli, Poisson, and Normal (univariate and multi-variate) data generating processes. For each process they consider how prior judgments about the uncertain parameters of the process are modified given the results of statistical sampling, and they investigate typical decision problems in which the main sources of uncertainty are the population parameters. They also discuss the value of sampling information and optimal sample sizes given sampling costs and the economics of the terminal decision problems. Unlike most introductory texts in statistics, this text integrates statistical inference with decision making and discusses real-world actions involving economic payoffs and risks. After developing the rationale and demonstrating the power and relevance of the subjective, decision approach, the text also examines and critiques the limitations of the objective, classical approach. 

 

An informal treatment of foundations; a formal treatment of foundations; assessment of utilities for consequences; quantification of judgements; analysis of decision trees; random variables; continuous lotteries and expectations; special univariate distributions; conditional probability and Bayes' theorem; Bernoulli process; terminal analysis - opportunity loss and the value of perfect information; paired random variables; preposterior analysis - the value of sample information; Poisson process; normal process with known variance; normal process with unknown variance; large sample theory; statistical analysis in normal form; classical methods; multivariate random variables; the multivariate normal distribution; choosing the best of several processes; allowance for uncertain bias; stratification; the portfolio problem; normal linear regression with known variance. Appendices: the terminology of sets; elements of matrix theory; properties of utility functions for monetary consequences; tables.