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A First Step toward a Unified Theory of Richly Parameterized Linear ModelsUsing mixed linear models to analyze data often leads to results that are mysterious, inconvenient, or wrong. Further compounding the problem, statisticians lack a cohesive resource to acquire a systematic, theory-based understanding of models with random effects.Richly Param

Like its predecessor, this second volume presents detailed applications of Bayesian statistical analysis, each of which emphasizes the scientific context of the problems it attempts to solve. The emphasis of this volume is on biomedical applications. These papers were presented at a workshop at Carnegie-Mellon University in 1993.

The past few years have witnessed dramatic advances in computational methods for Bayesian inference. As a result, Bayesian approaches to solving a wide variety of problems in data analysis and decision-making have become feasible, and there is currently a growth spurt in the application of Bayesian methods. The purpose of this volume is to present several detailed examples of applications of Bayesian thinking, with an emphasis on the scientific or technological context of the problem being solved. The papers collected here were presented and discussed at a Workshop held at Carnegie-Mellon University, September 29 through October 1, 1991. There are five ma­ jor articles, each with two discussion pieces and a reply. These articles were invited by us following a public solicitation of abstracts. The problems they address are diverse, but all bear on policy decision-making. Though not part of our original design for the Workshop, that commonality of theme does emphasize the usefulness of Bayesian meth­ ods in this arena. Along with the invited papers were several additional commentaries of a general nature; the first comment was invited and the remainder grew out of the discussion at the Workshop. In addition there are nine contributed papers, selected from the thirty-four presented at the Workshop, on a variety of applications. This collection of case studies illustrates the ways in which Bayesian methods are being incorporated into statistical practice. The strengths (and limitations) of the approach become apparent through the examples.

Like the first two volumes, this third volume of case studies presents detailed applications of Bayesian statistical analysis, emphasizing the sci­ entific context. The papers were presented and discussed at a workshop at Carnegie Mellon University, October 5-7, 1995. In this volume, which is dedicated to the memory of Morris H. DeGroot, econometric applica­ tions are highlighted. There are six invited papers, each with accompany­ ing invited discussion, and eight contributed papers (which were selected following refereeing). In addition, we include prefatory recollections about Morrie DeGroot by James o. Berger and Richard M. Cyert. INVITED PAPERS In Probing Public Opinion: The State of Valencia Experience, Jose Bernardo, who was a scientific advisor to the President of the State of Valencia, Spain, summarizes procedures that were set up to probe public opinion, and were used as an input to the government's decision making process. At the outset, a sample survey had to be designed. The problem of finding an optimal Bayesian design, based on logarithmic divergence be­ tween probability distributions, involves minimization over 21483 points in the action space. To solve it, simulated annealing was used. The author describes the objective of obtaining the probability that an individual clas­ sified in a certain group will prefer one of several possible alternatives, and his approach using posterior distributions based on reference priors.