OBJECTIVE BAYESIAN INFERENCE

Bayesian analysis is today understood to be an extremely powerful method of statistical analysis, as well an approach to statistics that is particularly transparent and intuitive. It is thus being extensively and increasingly utilized in virtually every area of science and society that involves analysis of data.

A widespread misconception is that Bayesian analysis is a more subjective theory of statistical inference than what is now called classical statistics. This is true neither historically nor in practice. Indeed, objective Bayesian analysis dominated the statistical landscape from roughly 1780 to 1930, long before 'classical' statistics or subjective Bayesian analysis were developed. It has been a subject of intense interest to a multitude of statisticians, mathematicians, philosophers, and scientists. The book, while primarily focusing on the latest and most prominent objective Bayesian methodology, does present much of this fascinating history.

The book is written for four different audiences. First, it provides an introduction to objective Bayesian inference for non-statisticians; no previous exposure to Bayesian analysis is needed. Second, the book provides an overview of the development and current state of objective Bayesian analysis and its relationship to other statistical approaches, for those with interest in the philosophy of learning from data. Third, the book presents a careful development of the particular objective Bayesian approach that we recommend, the reference prior approach. Finally, the book presents as much practical objective Bayesian methodology as possible for statisticians and scientists primarily interested in practical applications.

Contents:

• Preface
• Overview and Notation
• The Objective Bayesian Paradigm:
  • Basics of Bayesian Analysis
  • Basics of Objective Bayesian Analysis
• Select Early Objective Bayesian Developments:
  • The Constant Prior
  • Jeffreys-Rule Priors
  • Frequentist Matching
  • Invariance Priors
  • Evaluating Objective Priors
• Reference Analysis:
  • Introduction to Part III
  • Models with One Continuous Parameter
  • Multiple Continuous Parameters
  • Discrete Parameter Problems
  • Overall Objective Priors
  • Reference Priors with Partial Information
  • Models with Special Structures
  • A Catalog of Objective Priors
• A Common Distributions
• Bibliography
• Author Index
• Index

Readership: Undergraduate and graduate students, researchers in Statistics.

Key Features:

• The first modern presentation of Objective Bayesian inference
• The first complete development of the reference prior approach to objective Bayes
• Presents a needed overview of the fascinating 250 year history of objective Bayes
• Includes extensive discussion of the relationship of objective Bayes to subjective Bayes and classical statistics
• The material is arranged so that it can serve as an introduction to Bayesian analysis