| A PERSONAL HISTORY OF BAYESIAN STATISTICS | | | | Thomas Hoskyns Leonard | | | | Retired Professor of Statistics, Universities of Wisconsin-Madison and Edinburgh |
FIRST PUBLISHED ONLINE APRIL 2014
REVISED APRIL 2021 |
| | | | ABSTRACT | | | The history of Bayesian Statistics is traced, from a personal perspective, through various strands and via its re-genesis during the 1960s to the current day. Emphasis is placed on broad-sense Bayesian methodology which can be used to meaningfully analyse observed data sets. Over 750 people in Science, Medicine and Socio-Economics, who have influenced the evolution of the Bayesian approach into the powerful paradigm that it is today, are highlighted. The Frequentist/Bayesian controversy is addressed, together with the ways in which many Bayesians combine the two ideologies as a Bayes/non-Bayes compromise e.g. when drawing inferences about unknown parameters or when investigating the choice of sampling model in relation to its real-life background. A number of fundamental issues are discussed and critically examined, and some elementary explanations for non-technical readers and some personal reminiscences are included. Some of the Bayesian contributions of the 21 st. century are subjected to more detailed critique, so that readers may learn more about the quality and relevance of the ongoing research. A recent resolution of Lindley’s paradox by Baskurt and Evans is reported. The Axioms of Subjective Probability are reassessed, some state-of-the-art alternatives to Leonard Savage’s Axioms of Utility are discussed, and Deborah Mayo and Michael Evan’s [SINCE THOUGHT TO BE FALSE} refutation of Allan Birnbaum’s 1962 justification of the Likelihood Principle in terms of the Sufficiency and Conditionality Principles is addressed. | | | KEYWORDS: History of Bayesian Statistics, Thomas Bayes, Bayesian Inference, Bayesian model choice, Bayesian methodology, Frequentist/Bayesian controversy, Bayes/non-Bayes compromise, Bayesian model choice, Lindley’s Paradox, Marginalization paradox, Baskurt-Evans, axioms of subjective probability, Leonard Savage. Axioms of Utility. Michael Evans, Birnbaum’s proof, likelihood principle, sufficiency principle, conditionality principle, Dennis Lindley, subjective probability, statistical probability, inverse probability, Bayes factor, hierarchical Bayesian, empirical Bayesian, random effects models, spatial processes, multiple time series, MCMC, Metropolis-Hastings algorithm, Laplacian approximation, Daniel Bernoulli, Richard Price, Pierre-Simon de Laplace, Occam’s razor, expected utility hypothesis, Allais Paradox, decision theory, De Finetti axioms, Savage axioms, improper prior, Jeffreys prior, reference prior, Kalman filter, conjugate analysis, M-group regression, Bayesian analysis of categorical data, Bayesian semi-parametric methods, roughness penalty, Dirichlet prior, inverted Wishart prior, Importance Sampling, smoothing splines, cross-validation, AIC,BIC,DIC. statistical model checking and comparison, Bayesian Econometrics, stochastic volatility, measure of evidence, Bayesian genomics, legal statistics, Sally Clark case, DNA evidence, Alfred Dreyfus case, O.J. Simpson case, Adams rape case, Nurse Atkinson case, the Rosie and the ten construction workers case, Essen-Möller formula. | | | Address for correspondence: Thomas Leonard, 4/3 Hopetoun Crescent, Edinburgh EH7 4AY, Scotland
E-mail: leonardthomas70@googlemail.com, | | | ACKNOWLEDGEMENTS | | | Many thanks to Michael Evans, Angelika van der Linde, Peter Wakker, Tony O’Hagan, Fabrizio Ruggeri, Jim Smith, David Scott, Timothy Wallstrom, Murray Aitkin, David Balding, and John S.J.Hsu for their detailed advice and valuable contributions, and to Jim Dickey, Irwin Guttman, Nick Polson, Ming-Mei Wang and George E.P. Box for their various academic accounts from the past. | | | My former Ph.D. supervisor Dennis V. Lindley sadly passed away in Minehead, Somerset on 14th December 2013 shortly after this history was completed. I enthusiastically acknowledge the wonderful way he and Phil Dawid educated me at University College London, together with his unique insights about our enigmatic discipline. | | | 
| | In Memorium, Dennis V. Lindley (1923-2013) |
| | | Thanks also to James Carter, Scott Forster, Adam Trettel, Felix Waldmann, Cassie Strickland, Richard A. Johnson, Daniel Gianola, Stephen Fienberg, Grace Wahba, Norman Draper, Jim Albert, Kam-Wah Tsui, Michael Hamada, Julian Stander, Andrew Lawson, Richard Burton, Philip Brown, George Stretfaris, Colin Aitken, Philip Prescott, Orestis Papasouliotis, Matthew Stephens, Thomas Tallis, Deborah Mayo, Neil Chue Hong, Colin Reid, Dee Raspin, Adam Logan and various members of the Edinburgh All-Comers Writers Club for their helpful comments and input, the Celtic scholar Eystein Thanisch for translating a quote in medieval Latin by William of Ockham, and Ernest Gujer of Zurich for his helpful advice about the Swiss mathematician Daniel Bernoulli. The unexpectedly dramatic events surrounding my consultations with my colleagues have themselves become part of the history of Bayesian Statistics. |
| CONTENTS | | | THE FIRST FOUR ITEMS ARE PUBLISHED BY JOHN WILEY (Wiley Hot Article of the Week, April 2014) Related Interview in Statistics Views
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