A personal history of Bayesian statistics. (31st January 2014)

• Record Type: Journal Article
• Authors: Leonard, Thomas Hoskyns
• Is Part Of: Wiley interdisciplinary reviews. Volume 6:Number 2(2014)
• Page Start: 80
• Page End: 115
• Publication Date: 2014-01-31
• Subjects: 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 -- 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 -- Lindley's paradox -- Marginalization paradox -- 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 semiparametric 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 -- Bayesian Genomics -- measure of evidence -- 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; Mathematical statistics -- Data processing -- Periodicals; Science -- Data processing -- Periodicals; Social sciences -- Data processing -- Periodicals; Mathematical statistics -- Periodicals; 519.50285
• DOI: 10.1002/wics.1293
• Languages: English
• ISSNs: 1939-5108

Abstract

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 that can be used to meaningfully analyze observed datasets. Over 750 people in science, medicine, and socioeconomics, 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 nontechnical readers and some personal reminiscences are included. Some of the Bayesian contributions of the 21st 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 refutation of Allan Birnbaum's 1962 justification of the likelihood principle in terms of the sufficiency and conditionality principles is addressed. WIREs Comput Stat 2014, 6:80–115. doi: 10.1002/wics.1293 This article is categorized under: Statistical and Graphical Methods of Data Analysis > Bayesian Methods and Theory