A History of Markov Chain Monte Carlo* -Subjective Recollections from Incomplete Data- CHRISTIAN ROBERTT GEORGE CASELLA Universite Paris Dauphine and CREST,INSEE University of Florida August 14,2008 Abstract In this note we attempt to trace the history and development of Markov chain Monte Carlo (MCMC)from its early inception in the late 1940's through its use today. We see how the earlier stages of the Monte Carlo(MC,not MCMC)research have led to the algorithms currently in use.More importantly,we see how the development of this methodology has not only changed our solutions to problems,but has changed the way we think about problems. 1 Introduction Markov Chain Monte Carlo (MCMC)methods have been around for almost as long as Monte Carlo techniques,even though their impact on Statistics has not been truly felt until the very early 1990s.(The emergence of Markov based techniques in Physics and,in particular, Particle Physics is another story that will remain mostly untold within this survey.See Landau and Binder 2005 for a review.)Also,we will not launch into a description of MCMC techniques,unless they have some historical link,as the remainder of this volume covers *We are grateful for comments and suggestions from Olivier Cappe,David Spiegelhalter,Alan Gelfand, Jun Liu,Sharon McGrayne,Peter Muller,Gareth Roberts,and Adrian Smith Professor of Statistics,CEREMADE,Universite Paris Dauphine,75785 Paris cedex 16,France.Sup- ported by the Agence Nationale de la Recherche(ANR,212,rue de Bercy 75012 Paris)through the 2006-2008 project Adap'MC.Email:xian@ceremade.dauphine.fr. Distinguished Professor,Department of Statistics,University of Florida,Gainesville,FL 32611.Sup- ported by National Science Foundation Grants DMS-04-05543,DMS-0631632 and SES-0631588.Email: casella@stat.ufl.edu. 1A History of Markov Chain Monte Carlo∗ —Subjective Recollections from Incomplete Data— Christian Robert† Universit´e Paris Dauphine and CREST, INSEE George Casella‡ University of Florida August 14, 2008 Abstract In this note we attempt to trace the history and development of Markov chain Monte Carlo (MCMC) from its early inception in the late 1940’s through its use today. We see how the earlier stages of the Monte Carlo (MC, not MCMC) research have led to the algorithms currently in use. More importantly, we see how the development of this methodology has not only changed our solutions to problems, but has changed the way we think about problems. 1 Introduction Markov Chain Monte Carlo (MCMC) methods have been around for almost as long as Monte Carlo techniques, even though their impact on Statistics has not been truly felt until the very early 1990s. (The emergence of Markov based techniques in Physics and, in particular, Particle Physics is another story that will remain mostly untold within this survey. See Landau and Binder 2005 for a review.) Also, we will not launch into a description of MCMC techniques, unless they have some historical link, as the remainder of this volume covers ∗We are grateful for comments and suggestions from Olivier Capp´e, David Spiegelhalter, Alan Gelfand, Jun Liu, Sharon McGrayne, Peter Muller, Gareth Roberts, and Adrian Smith †Professor of Statistics, CEREMADE, Universit´e Paris Dauphine, 75785 Paris cedex 16, France. Sup￾ported by the Agence Nationale de la Recherche (ANR, 212, rue de Bercy 75012 Paris) through the 2006-2008 project Adap’MC. Email: xian@ceremade.dauphine.fr. ‡Distinguished Professor, Department of Statistics, University of Florida, Gainesville, FL 32611. Sup￾ported by National Science Foundation Grants DMS-04-05543, DMS-0631632 and SES-0631588. Email: casella@stat.ufl.edu. 1