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.

James Berger is the Arts and Sciences Professor Emeritus of Statistics at Duke University. Berger was president of the Institute of Mathematical Statistics from 1995–1996 and of the International Society for Bayesian Analysis during 2004. He was the founding director of the Statistical and Applied Mathematical Sciences Institute, serving from 2002–2010. He was co-editor of the Annals of Statistics from 1998–2000 and was a founding editor of the Journal on Uncertainty Quantification from 2012–2015. Berger received the COPSS 'President's Award' in 1985, was the Fisher Lecturer in 2001, the Wald Lecturer of the IMS in 2007, and received the Wilks Award from the ASA in 2015. He was elected as a foreign member of the Spanish Real Academia de Ciencias in 2002, elected to the USA National Academy of Sciences in 2003, was awarded an honorary Doctor of Science degree from Purdue University in 2004, and became an Honorary Professor at East China Normal University in 2011. Berger has published over 200 research papers and written or edited 16 books.

Jose M Bernardo is Emeritus Professor of Statistics, Universidad de Valencia, Spain. He is a fellow of the American Statistical Association and a member the Real Academia de Ciencias in Spain. He was the organizer of the Valencia International Meetings on Bayesian Statistics, held in 1979, 1983, 1987, 1991, 1994, 1998, 2002, 2006 and 2010; these were the premier world meetings on Bayesian analysis. Bernardo was the founding co-president of the International Society for Bayesian Analysis and was the founding coordinator of the European Master on Bayesian Statistics and Decision Analysis, a joint initiative of the universities of Helsinki, Klagenfurt, Madrid-Carlos III, Paris-Dauphine, Roma-La Sapienza and Valencia. He was the founding editor of Test and has been associate editor of 7 journals. Bernardo has published over 100 research papers and has authored or edited 12 books, including Bayesian Analysis (with AFM Smith).

Dongchu Sun is Professor of Statistics at East China Normal University. He is a fellow of the Institute of Mathematical Statistics and the American Statistical Association and is a recipient of the University of Missouri Chancellor's Award for Outstanding Research and Creative Activity in the Physical and Mathematical Sciences. He also received the Albert Winemiller Prize for Outstanding Research in Psychological Statistic. Sun was co-editor of Sankhya, Series B, and founding co-editor of Statistics and Related Fields. He also served on the editorial boards of for four other journals.