March 2010 the Oﬃcial Bulletin of the International Society for Bayesian Analysis

THE ISBABULLETIN

Vol. 17 No. 1 March 2010 The oﬃcial bulletin of the International Society for Bayesian Analysis

AMESSAGEFROMTHE related interests. The process to form a new sec- PRESIDENT tion is amazingly simple. Formally, all that is needed is a petition by 30 members to propose Peter Müller the bylaws and initial officers of a proposed sec- ISBA President, 2010 tion. The ISBA Board considers the proposal and [email protected] votes on the proposal. That’s all. I hope that I would first like to thank Mike West for his ser- ISBA/BNP will be followed by other section pro- vice as past president. Among many other issues posals. A natural focus point is any established Mike has provided invaluable service to ISBA series of workshops or other events. For exam- by revising and reviving our IT infrastructure. ple, for ISBA/BNP the organization of the BNP Many of you must have already used the nifty workshops is the natural purpose and activity of new on-line membership service. The elected the new section. new officers for 2010 and the new editors were Other exciting events in the upcoming year are already mentioned in the last Bulletin. In ad- several meetings organized and co-sponsored by dition to these new officers I welcome our new ISBA. Alex Schmidt is summarizing the many 2011 program chair Igor Pr ünster. Since join- upcoming meetings elsewhere in this Bulletin. If ing the program council in January Igor has al- you are. . . Continued on page 2. ready worked hard to help with the selection of the ISBA travel awards. Thanks! Another new appointment is David Dunson as the new chair In this issue of the Membership Committee. ® A MESSAGE FROM THE BA EDITOR We will soon begin the process to organize Page 3 the 2011 ISBA elections, starting with the forma- tion of the nomination committee. As laid out ® FROM THE PROGRAM COUNCIL in the ISBA bylaws the nomination committee is Page 4 chaired by the past president. All members are invited to make suggestions for membership in ® ANNOTATED BIBLIOGRAPHY the nomination committee. Please forward sug- Page 5 gestions to me. ® BAYESIAN HISTORY In the past years it has occasionally been pro- Page 7 posed to initiate sections in ISBA. The constitu- tion provides for the possibility of sections and ® APPLICATIONS the policy on sections lays out a very simple pro- Page 12 cess to launch sections. I believe that the for- mation of sections could be a wonderful oppor- ® SOFTWARE HIGHLIGHT tunity to keep ISBA relevant for our members, Page 16 and to ensure that ISBA activities continue to ® STUDENTS’ CORNER reflect the forefront of current developments in Page 18 Bayesian analysis. A specific proposal for an ISBA section on Bayesian nonparametrics (BNP) ® NEWS FROM THE WORLD is currently being prepared by some members. Page 18 There is a long running series of workshops that loosely defines a community of researchers with ISBA Bulletin, 17(1), March 2010

MESSAGE FROM THE PRESIDENT, Continued consider to nominate the paper for the Lindley from page 1. . . . involved in organizing any event Prize. related to Bayesian analysis, please consider to For the upcoming World Meeting we are include ISBA co-sponsorship. The rules for set- happy to be able to provide a large number of ting up ISBA co-sponsorship are laid out on travel awards. Supported from a variety of fund- our homepage http://www.bayesian.org (se- ing sources we are able to provide partial sup- lect ”ISBA business” and ”meetings”). port for 62 participants. This includes travel Surely the most important ISBA event in 2010 support from ASA/SBSS for the finalists of the is the ISBA World Meeting and Valencia Meet- jointly ISBA and SBSS supported Savage award, ing. The scientific program committee, chaired additional SBSS travel support for several senior by the 2009 program chair Herbie Lee, has done graduate students and young researchers within an outstanding job to prepare a stunning pro- 2 years of their Ph.D. degree. An important gram. The process included open submission of funding source is an NSF (US National Science abstracts and a blinded selection process. We are Foundation) conference grant that provides par- very happy to note that the resulting program in- tial travel support for 13 young US investigators. cludes a large percentage of young researchers, NIH (US National Institutes of Health) is provid- and thus naturally many new ideas. Please join ing partial travel support for 7 young US inves- us in particular for the Savage award session tigators who present cancer related work (The when the finalists for the Savage thesis award are award is still subject to final approval). This presenting. The Savage prize is jointly organized reflects the increasing importance of Bayesian by ISBA and ASA/SBSS (the Section on Bayesian statistics in biomedical research in general and in Statistical Science of the American Statistical As- cancer research in particular. More travel awards sociation). The Savage finalists session is a won- are supported by ISBA, including the Pilar Igle- derful opportunity to meet tomorrow’s leaders of sias travel fund to support participants from de- Bayesian statistics. veloping countries and the ISBA Lifetime Members The Savage prize is one of several prizes that Award. are awarded by ISBA. Besides the Savage Award One of the most important decisions for ISBA ISBA organizes and awards the De Groot Prize in the upcoming year is the choice of the site for a book in statistical science, the Lindley Prize for the 2012 ISBA World Meeting. We have re- for the best contributed paper presented at the ceived several excellent pre-proposals and have World Meeting, and the Mitchell Prize for the best invited representatives for each pre-proposal to applied Bayesian paper. Please watch out for the present their proposals during the upcoming announcements for submissions for these prizes. World Meeting in Benidorm. The proposals will In particular, we will consider a re-organization be discussed in the General Member Meeting and of the submission process for the Lindley Prize. If a final choice will be made by the Board. ISBA you notice a particularly outstanding paper pre- has the wonderful problem of chosing between sented at the upcoming World Meeting, please several outstanding alternatives! L

AMESSAGEFROMTHE EDITOR Editors. I am now delighted to continue these ef- forts. First, I want to thank Rapahel Gottardo for his work as Editor and for the advice and help Manuel Mendoza he has provided me during this transition. I also [email protected] want to thank Mayetri Gupta who last December finished her term as Associate Editor of the Ap- In November 1992, the first issue of this Bulletin plications section. On the other hand, I can say appeared as the ISBA NEWSLETTER under the that it has been a pleasure to work on the pro- editorship of Tom Leonard. During almost 18 duction of this first 2010 issue. The team of As- years, we have all witnessed the steady improve- sociated Editors that have, very kindly, agreed to ment of this means of communication of our so- continue their work for the Bulletin are quite ex- ciety. This achievement has been possible only perienced and this makes my task enjoyable. I because of the collaboration of all in the Bayesian am sure that we will produce a Bulletin with the community and the enthusiastic work of the past quality standard that our community requires

Content 2 www.bayesian.org ISBA Bulletin, 17(1), March 2010 BAYESIAN ANALYSIS - A MESSAGE FROM THE EDITOR and that several new proposals will emerge from by Ciprian Crainiceanu explores the analysis of our ongoing exchange of ideas. complex data from a different perspective. I also In this number, you will find most of the usual hope you will find interesting the contribution sections with interesting information. Particu- by Tapen Sinha and myself on the History of larly, I would like to call your attention to the Bayesian Statistics. article by Marc Suchard, Chris Holmes and Mike I want to encourage all members of ISBA to West on graphic processing unit computing. This contribute with their suggestions and specific is a timely introduction to a rather new ap- manuscripts and announcements for the existing proach to massive computing, whose long-term sections. Please do not hesitate to contact any impact in Bayesian Analysis is highly promis- member of the Editorial Board. Finally, I also ing. We thank the authors for bringing this in- want to thank Pedro Regueiro for his technical novative subject to our Bulletin. In close re- assistance with the typesetting of this Bulletin. L lation, the article on Bayesian functional data

BAYESIAN ANALYSIS - A MESSAGE FROM THE EDITOR

FIRST WORDS Sivia give additional context for the problem and the methodology. The remainder of the issue fea- Herbie Lee tures seven other fine articles on topics from pri- Editor-in-Chief ors to methodology to an application in medical [email protected] image analysis. We have a great team assembled on our edi- I am greatly honored to be following Rob Kass torial board, and I am grateful for all their help. and Brad Carlin as the next Editor-in-Chief of I am particularly thankful that Pantelis Vlachos Bayesian Analysis, our society’s journal. They is continuing on as system managing editor, as have done a great job launching and growing the he continues to be invaluable in the running and journal, and I hope to continue its upward trajec- production of the journal. I am also thankful tory. We just published our first issue of Volume that production editor Angelika van der Linde 5, have recently joined the Science Citation Index, is continuing, and that Alyson Wilson is joining and we are looking forward to receiving our first us as the new managing editor. Our wonderful impact factor in 2010. set of editors are Kate Cowles, David Dunson, Our new issue features a discussion paper in- David Heckerman, Michael Jordan, Antonietta troducing a Bayesian approach for the analysis of Mira, Bruno Sanso,´ Mark Steel, and Kert Viele, small-angle neutron scattering experiments. This and we have a large team of great associate edi- paper by Charles Hogg, Joseph Kadane, Jong Soo tors. Lee, and Sara Majetich was originally chosen as We look forward to your submissions (and to one of the invited case studies for the 2009 Case your help with occasional requests for reviews). Studies in Bayesian Statistics and Machine learn- Bayesian Analysis publishes articles in all areas ing Workshop, and the Bayesian approach allows of Bayesian statistics, from theory to methodol- the authors to gain new insights relative to the ogy to case studies, as well as other types of in- traditional methodology. Discussions by Nick sightful articles. If you have any questions or Hengartner and by John Skilling and Devinder suggestions, please let me know. L

Content 3 www.bayesian.org ISBA Bulletin, 17(1), March 2010 FROM THE PROGRAM COUNCIL

FROM THE PROGRAM COUNCIL

ISBANEWS • Student Video Competition Alexandra M. Schmidt, Herbie Lee & Igor This year, the ISBA Student Video Compe- Prüenster tition gave PhD students a unique opportunity to win travel funding to attend ISBA If you are thinking about proposing a site 2010. The challenge was for students to cre- for an ISBA meeting then we encourage you ate a video describing their PhD research to refer to the ISBA Program Council Proce- that appealed to undergraduate students dures (http://www.bayesian.org/business/ interested in a career in statistics. With newmeetingsprocedures.html) on meetings, initial entry based on abstract submission, which provides the guidelines that will be used short listed entries were invited to submit to recommend venues for these meetings. We are 3-5 minute video to be judged by students currently (co-)sponsoring the following meet- and members of the ISBA 2010 Organizing ings: Committee. The final videos were of extremely high quality, including everything ISBA 2010 World Meeting/9th Valencia Meeting from animation to supervisor cameo ap- pearances. For all attending ISBA 2010, a The ISBA 2010 World Meeting will be held selection of videos will be screened at the in conjunction with the Ninth Valencia Interna- contributed talk sessions. tional Meeting on Bayesian Statistics from June 3 • to June 8, 2010 in Benidorm, Spain. We believe ISBA Travel awards we have an exciting program covering a wide We received over 150 applications, but range of subjects. The program comprises con- we had limited funds and are support- tributed talks and poster sessions. We have also ing around 40 awards, covering appli- organized a Student Video competition. Below cants from different locations in the world, follows more details: e.g. Singapore, South Africa, Chile, Brazil, Spain, Portugal, UK, USA. • Contributed Talks We received 164 abstracts for 36 con- Regional Meetings of ISBA Local Chapters tributed talks, so the process was highly competitive. We conducted blinded re- EBEBX (www.dme.ufrj.br/ebebx), the 10th views, with each submission read and Brazilian Bayesian meeting, will be held from scored by two members of the program the 21st until the 24th of March, 2010 in Angra committee, and the top scorers were or- dos Reis, in the state of Rio de Janeiro. ganized into nine coherent sessions. We note that two-thirds of the selected talks Co-sponsored and Endorsed Meetings are new researchers, and almost half of • Frontiers of Statistical Decision Making those are current students. These pro- and Bayesian Analysis (in honor of James portions are over-represented compared Berger) http://bergerconference2010. to the submission pool, so we think the utsa.edu/ will take place March 17-20, blinding worked well in helping us se- 2010 in San Antonio, Texas, USA. lect cutting-edge talks. We are looking forward to a great program which can • A Workshop on Model Uncertainty be checked at http://www.bayesian.org/ (http://www2.warwick.ac.uk/fac/ events/isba2010/schedule.html. sci/statistics/crism/workshops/ • Posters model-uncertainty/), hosted by CRiSM, will take place May 30 - June 1, 2010 at the We have received over 370 abstracts for University of Warwick. posters presentations. These will be presented in five sessions, every evening from • The Carlo Alberto Stochastics Workshop June 3rd through June 7th. (http://www.carloalberto.org/stats_

Content 4 www.bayesian.org ISBA Bulletin, 17(1), March 2010 ANNOTATED BIBLIOGRAPHY

workshop.html) will take place June 11, • International Research Conference 2010 in Moncalieri, Italy. on Bayesian Learning (http://marc. yeditepe.edu.tr/yircobl11.htm) will • The CBMS Conference on Bayesian Non- take place in Istanbul Turkey during June parametric Statistical Methods (http:// 10-12, 2011. It will celebrate the 310th an- www.ams.ucsc.edu/CBMS-NPBayes) will niversary of the birth of Reverend Thomas take place August 16-20, 2010 in Santa Bayes, in Istanbul. Cruz, California, USA. • The Eighth ICSA International Conference ISBA Topic Contributed Session at JSM, Van- (http://www.icsa2.org/Intl_2010/) will couver, August 2010 take place December 19-22, 2010 in Guangzhou, China. This ISBA session is sponsored by the Sec- tion on Bayesian Statistical Science (SBSS) of • AdapskIII (http://www.maths.bris.ac. the American Statistical Association (ASA). This uk/~maxca/adapskIII/), the satellite meet- year the theme of the session is “Bayesian In- ing to MCMSki III, will take place January ference in Massive Data Problems”. The speak- 3-4, 2011 in Park City, Utah, USA. ers are: Christian Robert (Universite´ Paris- • MCMSki III (http://madison.byu.edu/ Dauphine, France), Long Nguyen (University of mcmski/) will take place January 5-7, 2011 Michigan, USA), Yuan Ji (MD Anderson Cancer in Utah, USA. Center), and Bhramar Mukherjee (University of Michigan, USA). The discussant is Michele Guin- • A Conference in Honour of Professor dani from The University of New Mexico, USA. Adrian F. M. Smith on Hierarchical Mod- els and Markov Chain Monte Carlo (http: L //www.afmsmith.com/) will take place June 2-5, 2011 in Heraklion, Greece.

ANNOTATED BIBLIOGRAPHY

PRIORDISTRIBUTIONSFOR than shrank towards. Indeed, In a parallel way, COVARIANCE/PRECISION the covariance parameter does not belong to the MATRICES, PART 2 cone of positive definite matrices but rather to the cone QG of incomplete partially positive def- HélèneMassam1 inite matrices with entries missing according to Department of Statistics G. By ”partially positive definite”, we mean that York University, Canada. any submatrix corresponding to a complete sub- [email protected] graph of G is positive definite. The number of parameters to be estimated is thus reduced and In this issue we continue our consideration of graphical Gaussian models have become an es- priors for covariance matrices. The last issue sential tool in the analysis of high-dimensional was devoted to priors on full matrices. Graph- data, especially in a ”large p, small n” situation. ical models, developed after the seminal work Working in QG gave rise to the analog of the in- by Dempster (1972), take a slightly different tack verse Wishart on QG, a distribution called the hy- on the covariance estimation problem. In graphi- per inverse Wishart (Dawid and Lauritzen, 1993). cal Gaussian models, the precision parameter be- Like its analog, the hyper inverse Wishart suffers longs to the cone PG of positive definite matrices from the fact that it only has one shape parame- with fixed zeros according to the missing edges ter. Some work has been done to study shrink- in the graph G underlying the graphical Gaus- age properties for priors on PG or QG but much sian model.The main task is model selection in remains to be done. the class of graphical Gaussian model, and once a model is chosen, the structure is imposed rather • Dempster, A. (1972) Covariance selection, 1This author was supported by NSERC grant A 8947.

Content 5 www.bayesian.org ISBA Bulletin, 17(1), March 2010 ANNOTATED BIBLIOGRAPHY

Biometrics, 28, 157-175. A seminal paper posterior) has to be computed numerically. for graphical Gaussian models. The reduc- This computation is crucial in graphical tion of the number of parameters in the co- Gaussian model selection and has been the variance matrix is achieved by expressing subject of much research. Sampling from conditional independences between com- the posterior is not considered in the pa- ponents of the Gaussian model as zeros in per but can be done using Bayesian itera- the precision matrix. tive proportional ﬁtting.

• Dawid, A.P. and Lauritzen, S.L. (1993) Hy- • Wong, F. and Carter, C.K. and Kohn, R. per Markov laws in the statistical analysis (2003), Efﬁcient estimation of covariance se- of decomposable graphical models, Ann. lection models, Biometrika, 90, 809-830. This Statist., 21, 1272-1317. The authors intro- paper uses a decomposition of the DRD duce the concept of hyper Markov laws. type for the precision matrix in graphical Applied to the covariance parameter of Gaussian models Markov with respect to graphical Gaussian models Markov with an arbitrary graph, thus constraining the respect to a decomposable graph, this con- entries of the R matrix corresponding to cept roughly means that the conjugate prior missing edges to be 0. The Dt are assumed for the covariance parameter (recall this i.i.d. Gamma(α, β). A hierarchical prior parameter belongs to QG) can be writ- for the R matrix taking into account the to- ten as a Markov combination of conju- tal number of nonzero entries in R˜ leads to gate priors for the covariance parameters heavy computations for the posterior. of the marginal distribution of the Gaus- sian model for cliques and separators of • Andersson, S.A. and and Wojnar, G.G. the graph. For the marginal distributions (2004) Wishart Distributions on Homoge- on the cliques and separators, these con- neous Cones, Journal of Theoretical Proba- jugate priors are inverse Wisharts and the bility,17, 781-818. Though no prior is for- prior on Σ in QG is called the hyper in- mally offered in this paper, the authors give verse Wishart. This prior is conjugate in the expression of the Wishart distribution the sense of Diaconis-Ylvisaker. The nor- on homogeneous cones which can include malising constant can be obtained analyt- some of the priors given in Sun and Sun ically and sampling from the posterior is (2005) as extreme cases and coincide with easy and does not require MCMC tech- the results of Letac and Massam (2007) for niques. It also has the very useful prop- homogeneous graphs. erty of being strong hyper Markov which means that computations can be done lo- • Sun, D. and Sun, X. (2005) Estimation of the cally within each clique. However, like the multivariate normal precision and covari- inverse Wishart, it only has one shape pa- ance matrices in a star-shape model, Ann. rameter. This is a remarkable paper which Inst. Statist. Math., 57, 455 - 484. The au- is a seed paper for most subsequent studies thors consider a Gaussian model Markov on prior distributions for graphical models. with respect to a star-shaped graph which is a particular type of homogeneous graph. • Roverato, A. (2002) Hyper Inverse Wishart These graphs themselves form a subclass distributions for nondecomposable graphs of the class of decomposable graphs. The and its application to Bayesian inference corresponding Gaussian models are invari- for Gaussian graphical models, Scand. J. ant under the action of the group of lower Statist., 29, 391-411. The author identi- triangular matrices with zeros where edges ﬁes the Diaconis-Ylvisaker conjugate prior are missing in the star-shaped graph. The for the precision parameter Σ−1 for graph- authors work out the right and left invari- ical Gaussian models Markov with respect ant measures under that triangular group to an arbitrary (not necessarily decompos- as well as the reference priors under a given able) undirected graph and derives the in- grouping of the elements of the Cholesky duced prior on Σ. He shows that in the decomposition Σ−1 = T tT where T is lower case of a decomposable graph, this induced triangular. The Bayes estimators of Σ and distribution is the hyper inverse Wishart. Σ−1 under the various objective priors can The normalising constant of this prior (and be obtained explicitly.

Content 6 www.bayesian.org ISBA Bulletin, 17(1), March 2010 BAYESIAN HISTORY

• Letac, G. and Massam, H. (2007) Wishart graphical Gaussian models, Ann. Statist., distributions for decomposable graphs, 36, 2818–2849. This paper deﬁnes the Bayes Ann. Statist., 35, 1278-1323. The authors estimators under various losses and the

identify the inverse of the hyper inverse IWPG . These are the posterior means of −1 Wishart (the G-Wishart for decomposable Σ and Σ under the IWPG and WPG re- graphs) as an exponential family generated spectively and are given explicitly. A ref- by a measure which depends upon one pa- erence prior for Σ is also worked out and rameter only. Using a generalization of the risk properties of these estimators un-

this measure with k + 1 shape parameters der the hyper inverse Wishart, the IWPG for where k is the number of cliques of the un- various values of the shape and scale pa- derlying decomposable graph G, they de- rameters and the reference prior are stud-

ﬁne a more ﬂexible Wishart family on PG ied. The IWPG compares favorably with

called the WPG The shape parameters are the other priors and its ﬂexibility is illus- taken so that the normalising constant is trated with several examples. There is explicit and of the same general form as also empirical evidence that with the right that of the G-Wishart. The inverse of the choice of hyperparameters, the eigenvalues

WPG , the IWPG , is shown to be conjugate of the Bayes estimator under the IWPG can for the covariance parameter Σ ∈ QG. The be made to closely ﬁt the true eigenvalues.

IWPG offers conjugacy and flexibility for the shape parameters. It is also strong di- • Khare,K. and Rajaratnam, B. (2009), rected hyper Markov. The induced prior on Manuscript. A family of conjugate prior the φ and D parameters is also derived. For distributions is given for the covariance the complete model, the prior on (φ, D) co- parameter of graphical Gaussian models incides with that of Brown et al. (1994) or with Σ ∈ P , that is, marginal indepen- Consonni and Veronese (2003). Sampling G dence models Markov with respect to the from the posterior distribution of Σ is easy decomposable graph G. The number of and does not require MCMC techniques. A shape parameters is equal to the dimension generalized Wishart on Q is also defined G of the Gaussian vector. This family there- and can be considered as a prior (though fore offers flexibility as well as conjugacy. not conjugate) for the covariance parame- However, the normalizing constant has to ter of marginal independence models. be computed numerically and sampling • Rajaratnam, B., Massam, H. and Carvalho, from the posterior is done through a Gibbs C., (2008) Flexible covariance estimation in sampler.L

BAYESIAN HISTORY

LEONID HURWICZANDTHE Introduction TERM “BAYESIAN” ASAN ADJECTIVE Justifiably, Fienberg (2006) wrote the first paper in the first number of the electronic journal Bayesian Analysis. His purported purpose was to Manuel Mendoza elaborate on the term “Bayesian” as an adjective. Instituto Tecnológico Autónomode México In the process of his elaboration, Professor Fien- [email protected] berg produced a fine analysis of the history of & what we know today as Bayesian Statistics. His Tapen Sinha bibliography is extensive with 184 items. Some Instituto Tecnológico Autónomode México, of them (like his correspondence with Jack Good University of Nottingham, UK and John Pratt) are in the form of personal cor- [email protected] respondence. He takes us on a marvelous jour- ney of two hundred years of history of Bayes and Bayesian thinking. He divides the history

Content 7 www.bayesian.org ISBA Bulletin, 17(1), March 2010 BAYESIAN HISTORY into three distinct phases. First came Bayes Situation 1: Choose between and Laplace with a reminder of Stigler’s Law of Eponymy (”no scientific discovery is named after Gamble 1: 500, 000 with probability 1; and its original discoverer”). Then, as a precursor to Gamble 2: 2, 500, 000 with probability 0.1, the modern development, he discussed contribu- 500, 000 with probability 0.89, sta- tions during the first five decades of the Twen- tus quo with probability 0.01. tieth Century. Finally, he brought in the Neo- Bayesian Revival of the 1950s. Fienberg quotes Situation 2: Choose between from Lindley (2000), “When I began studying Gamble 3: 500, 000 with probability 0.11, sta- statistics in 1943 the term ‘Bayesian’ hardly ex- tus quo with probability 0. 89; and isted; ‘Bayes’ yes, we had his theorem, but not Gamble 4: 2, 500, 000 with probability 0.1, the adjective.” Fienberg also notes that Good status quo with probability 0.90. (1950) “writing on the weighing of evidence using Bayes‘ Theorem, in the third paragraph of the Savage chose gambles 1 and 4 respectively. Al- preface used the phrase ‘subjective probability lais noted that it contradicted expected utility judgments,’ but nowhere in the book [of Good‘s theory—the very foundation of a rational deci- book published in 1950] did he use the adjective sion maker of The Foundations of Statistics! As ‘Bayesian’.” Fienberg also notes that the usage we all know, in the book, Savage goes on to de- of the term ”Bayesian” was published during scribe why such a choice was not rational (even 1950–1951: One by Ronald Fisher in 1950 (in a though he himself made the choice initially). pejorative way) and by Jimmie Savage in 1951 A small exchange like this could have just where he used the phrase “unBayesian” (Savage, been a curiosity—a footnote in the history of eco- 1951, p. 58). Neither usage would count as we nomics. But it did not turn out that way. Allais use the term today as an adjective. Fienberg then went on to develop the theory of Non-Expected writes “[a] search of JSTOR reveals no earlier Utility for which he, and later Daniel Kahne- usage in any of the main American and British man, went on to win Nobel Prizes in Economics statistical journals.” He then goes on to sug- (Amos Tversky—a close collaborator of Kahne- gest that it was Jimmie Savage that brought the man would also have won the prize had he not Bayesian adjective to the fore. In what follows, died before the prize was awarded). Thus, we we will discuss the role that economists have contend that Jimmie Savage strongly influenced played during the critical period of the develop- the critical development of economic theory as a ment of the Neo-Bayesian Revival along with the whole. To prove our point, we did some bean- contribution of Jimmie Savage in economics. In counting. There were slightly less than one thou- particular, we point out the contribution of the sand references to Savage’s book in JSTOR (late 2007 Nobel Prize winner in Economics, Professor 2008). Of them around 30 percent were in eco- Leonid L Hurwicz. nomics journals. For sure, some of them occurred in journals that were right in the intersection of Jimmie Savage and Economics these two disciplines: Economics and Statistics. A classic example is Chernoff (1954). He refers to Fienberg justifiably examines Savage’s book Savage’s “Notes on the Foundations of Statistics” “The Foundation of Statistics” as a milestone for with the comment that it would be published in a the Neo-Bayesian Revival. It is striking that the book form. In turn, Savage’s research was also in- first five chapters of the book could very well fluenced by economics. To wit, around a quarter have been called “The Foundation of Economic of his references are directly from the economics Theory Under Risk and Uncertainty.” It begins literature. In contrast to mainstream economics, with the (Expected) Utility Theory—which has Savage’s book was not very well received by become the cornerstone of modern micro and many classical statistical theorists. For example, macro economic theories of today. Savage’s book Chung (1955) reviewed the book with the follow- did more than provide the foundation of modern ing comment. “A book like this is necessarily economic theory. His book (unwittingly) propa- part philosophy, and one who is not philosophi- gated an expansion. For example, in 1952, at the cally bent, as Mr. Savage clearly is, is often hard Econometric Society’s meeting in Paris, Maurice put to tell between what is critical thinking and Allais, presented Savage (and other participants) what is quibbling about words. To such a person with the following hypothetical choices. a good part of the discussion of the foundations

Content 8 www.bayesian.org ISBA Bulletin, 17(1), March 2010 BAYESIAN HISTORY of probability is typified by the following two ex- of decision making under risk and uncertainty. amples. 1. Re probability: when a coin is tossed More on Bayesian work at the Cowles Com- there is besides head and tail the possibility of mission can be found in Fienberg and Zellner the coin’s standing on its edge or disappearing (1975). The Cowles Commission for Research into a crevice. (For a variation on this theme see in Economics started in Colorado Springs be- p. 15 on whether a rotten egg spoils an omelet.) tween 1932 and 1938, operated at the Univer- 2. Re utility: some people gamble for a monetary sity of Chicago between 1939 and 1954, before loss in order to kill time or to cultivate good rela- moving to its permanent home at Yale Univer- tions. (For a variation see p. 101 on the show-off sity. When it moved to Yale, it had changed its flier.) I do not know how to draw a line between name to Cowles Foundation for Research in Eco- such bull session stunts and more serious argu- nomics.2 Hildreth (1981) provides a history of mentationE”´ To contrast the impact of Savage’s the Commission during this period. book on Statistics, we counted the number of citations it received in the Statistics literature. Leonid Hurwicz and the Bayesian ad- The total count in JSTOR is 483 (end of 2006). jective Of them, around 24 percent occurred during the 1980s—the time during which the Bayesian con- Hurwicz was a remarkable man. He was born cept received a big boost from computational in Moscow in 1917, grew up in Poland, survived breakthroughs. Comparing JSTOR citations in the Holocaust by just a hair, took the last boat economics versus statistics can be tricky. There to leave Europe to arrive in New Jersey with no are twice as many economics journals in JSTOR. money and a degree in Law from the Univer- sity of Warsaw. That was his only degree he The Cowles Commission in Chicago ever earned (apart from honorary degrees from a number of universities). Yet he went on to be- Nobel Prizes in Economics have been awarded come one of the foremost economic theorists of since 1969. And the list of names participat- the Twentieth Century and the oldest recipient of ing in the Cowles Commission who have won a Nobel Prize in any subject (at the age of 91). He the Nobel Prize is long. The list includes (with also became the only person to have received a the year of the award in parenthesis): Tjalling Nobel Prize without ever formally studying eco- Koopmans (1975), Kenneth Arrow (1972), Her- nomics (Sinha, 2008). bert Simon (1978), Gerard Debreu (1983), Franco Before Savage joined the University of Modigliani (1985), Harry Markowitz (1990), Chicago’s newly founded Statistics Department Trygve Haavelmo (1989), James Tobin (1981), in 1949, Hurwicz was already there. He became Edmund Phelps (2006), Joseph Stiglitz (2001), a Research Associate at the Cowles Commission Lawrence Klein (1980) and Leonid Hurwicz in 1942.3 During the war, Hurwicz was moon- (2007). Thus, about one in five of Nobel Prize lighting: teaching electronics to the U.S. Army winners in Economics were associates of the Signal Corps at the Illinois Institute of Technol- Cowles Commission. It is also noteworthy that ogy. At the University of Chicago, he was a mem- Savage’s book includes references to two member of the faculty of the Institute of Meteorology bers of this Cowles-Nobel list above (Arrow and and taught statistics in the Department of Eco- Markowitz). The Cowles Commission for Re- nomics. He worked under Jacob Marschak and search in Economics emerged as the second most Tjalling Koopmans at the Cowles Commission influential institution in economics (after the Na- for Research in Economics and Statistics at the tional Bureau of Economic Research) both at the University of Chicago. policy level and more importantly, for its contri- His work overlapped with what Savage was bution to economic theory. In the late 1940s and doing. This fact is evident from the Cowles Com- early 1950s, it was a hotbed of research in both mission Annual Report of 1950–51: ”. . . Many economics and statistics. Thus, it is not surpris- statisticians feel that, in their own practice, they ing to find that researchers there were intensely have to choose a ‘decision function’ (i.e., they working on Bayesian issues. In particular, Leonid have to design a sample or an experiment and Hurwicz was working on Bayesian formulations derive in advance a formula relating action to ob-

2We are indebted to Kenneth Arrow for pointing out this important distinction between the two entities: the Cowles Com- mission and the Cowles Foundation. 3http://cowles.econ.yale.edu/P/reports/1942.htm

Content 9 www.bayesian.org ISBA Bulletin, 17(1), March 2010 BAYESIAN HISTORY servation) without any advance knowledge as to dated December 25, 1950, Hurwicz (1950a) devel- the relative probabilities of alternative states of ops a technique of estimation using Bayes Theo- nature. The same is true of many practical sit- rem. In discussing the method, he remarks, “The uations. In fact, only in exceptional cases (such foregoing techniques . . . can be applied to justify as life insurance, games of chance, and scientific (from the Bayesian point of view) the maximum predictions based on much past experience) does likelihood method of estimation of the mean µ of the decision-maker have good information on the a normal distribution with a known variance σ2”. relevant probabilities. In the general case, such At around the same time, Hurwicz (1950b) information is not available; hence moral expec- noted “At the opposite extreme there exists the tation cannot be computed. Additional criteria ‘Bayesian’ formulation, where it is assumed that become necessary. Thus a pessimist will assume a probability measure ξ on ϑ (an ‘a priori distri- the worst possible state of nature to be true and bution’) is known to the statistician.” hence will maximize the lowest possible moral The main contribution, for which Hurwicz expectation; while, as pointed out by Franco shared his Nobel Prize with two others (Roger Modigliani, the optimist will maximize the max- Myerson and Eric Maskin), was pioneering work imum moral expectation. Leonid Hurwicz for- on Mechanism Design. He also received the Na- mulated a certain compromise between the two tional Medal of Science in 1990 in Behavorial and attitudes. In general, the compromise may be Social Science “for his pioneering work on the slanted toward optimism or pessimism, the ex- theory of modern decentralized allocation mech- tent of the slant being part of a person’s ‘tastes’. anisms”. He became the only economist to re- Another criterion was suggested by L. J. Savage ceive that honor before winning the Nobel Prize. and, independently, by Jurg Niehans of Zurich: This shows the diversity of Hurwicz’s research. for any given state of nature define as ‘loss’ (or On more than one occasion, researchers have ‘regret’) the difference between the highest moral discovered results only to find that Hurwicz was expectation that could be obtained if that state there first. He was a true scientific “Kilroy”. For were known and the moral expectation obtained example, in an interview, Jack Good once noted from a given action; then choose the action for that after he introduced the notion of hierarchical which the highest loss is lower than for any other Bayesian analysis: “the econometrician, L. Hur- action.”4 wicz, turned out to have published an abstract In the paper referred to in the previous para- a few months before my 1951 paper, suggesting graph, Hurwicz (1951a) introduced his famous the minimax exampleE”´ (Banks, 1996). Not only “alpha” that mitigated between minimax and did Hurwicz use the term “Bayesian” as an ad- maximax rules of decision. Milnor (1951) in his jective in his research papers in the early part of now famous RAND Research Memorandum ex- 1950s, he was already using these notions for the panded upon this rule. On page 2 of the same course he was teaching in the statistics depart- paper, Hurwicz notes: “The solution has been ment at the University of Minnesota. The follow- called ‘Bayesian’ (or ‘Bayes Optimal’) with re- ing paragraph reproduces the first question in the gard to H(0)(b).” Thus, already in February of PhD prelim examination in December 1953 writ- 1951, we have documented proof that Hurwicz ten by Hurwicz. was using the term Bayesian as an adjective. In a subsequent Discussion Paper, Hurwicz (1951b) A has two coins (c1, c2) of identical mentions “the Bayesian case” once more. Thus, appearance but different weight and not only was he using the phrase Bayesian as an weight distribution. B his permitted adjective, he was also anticipating the difference to observe one of the coins and is then between Bayesian and non-Bayesian cases in the required to guess whether it was c1 or ambit of decision making under uncertainty. In c2. He knows that the probability of footnote 1 of the same paper, he notes, “The more heads is 1/3 for c1 and 3/4 for c2 usual procedure is first to form a ‘risk function’ (a) List all the possible non- ρ(I , Ψ) ρ F with depending on the statistician’s randomized decision functions; preferences when ϑ3∗ is of the Bayesian type”. Is that the earliest reference to a clearly doc- (b) Indicate inadmissibility if found; umented Bayesian we find in the Neo-Bayesian (c) Find the maximum likelihood Revival movement? The answer is no. In a paper solution; 4http://cowles.econ.yale.edu/P/reports/1950-51a.htm

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(d) Find a Bayesian solution; and accuracy by comments from Stephen Stigler, (e) Find a minimax solution. Stephen Fienberg and above all, Kenneth Arrow. Additional help from Samiran Banerjee is also (In the later two cases, make such gratefully acknowledged. However, all errors additional assumptions as necessary.) are our own. Our original goal was to present Show that (c) is a special case of this paper to Professor Leonid L Hurwicz for his Bayesian solution. 92nd birthday. Unfortunately, Professor Hurwicz passed away on 24 June 2008. We would like to This example shows that Hurwicz propagated dedicate this paper in the memory of Professor the notion of Bayesian Statistics to the next gener- Leonid Hurwicz—an outstanding scholar, an ex- ation of students. Some of these students went on cellent teacher and above all, a great human be- to become outstanding econometricians in their ing. L own rights. Indeed, one such shining example was Daniel McFadden who went on to win a No- bel Prize in Economics for his work on discrete References choice econometrics. In fact, in his econometrics class notes5 dated April 8, 1952 Hurwicz clearly [1] Banks, D. L. (1996). A Conversation with distinguishes between three Bayesian concepts: I. J. Good. Statistical Science, 11 , 1–19. Bayesian, Parametric Bayesian and Generalized Bayesian (see pages 15–18 of the aforementioned [2] Chernoff, H. (1954). Rational Selection of document). Decision Functions. Econometrica, 22 , 422– 443.

Final Remarks [3] Chung, K. L. (1955). Review of L. J. Sav- age, The Foundation of Statistics. Bull. Amer. We provided evidence that Leonid Hurwicz Math. Soc., 61 , 236–239. might be the first person to have used the term Bayesian as an adjective. We have shown that [4] Fienberg, S. E. (2006). When did Bayesian In- during the Neo- Bayesian Revival, a strong inter- ference become Bayesian? Bayesian Analysis, action took place among Economists and Statis- 1 , 1–40. ticians: the ideas of an axiomatic foundation for the rational behavior of an economic agent on [5] Fienberg S. E. and Zellner, A. (eds). (1975). one hand, as well as for the coherent production Studies in Bayesian econometrics and statistics: of statistical inference, on the other. They were In honor of Leonard J. Savage. Amsterdam: essentially variations of the same theme. In the North Holland. case of Economics, the resulting criteria of max- imizing the expected utility came to occupy the [6] Good, I. J. (1950). Probability and the Weighing central stage of modern (neoclassical) economic of Evidence. London: Charles Griffin. theory. On statistical theory, the effect was some- [7] Hurwicz L. (1950a). Bayes and Minimax In- how different. The Neo-Bayesian Revival led to terpretation of the Maximum Likelihood Es- a new paradigm: the axiomatic development of timation Criterion. Cowles Commission Dis- Bayesian Theory of Statistics. cussion Paper Statistics 352. December 15, Acknowledgements 1950. [8] Hurwicz L. (1950b). Some Specification This work was partially supported by the Sis- Problems and Applications to Econometric tema Nacional de Investigadores, Mexico. Both Models. Report of the Chicago Meeting of the authors also acknowledge support from the Aso- Econometric Society. December 27–30, 1950. ciacion Mexicana de Cultura, A. C. Key information regarding unpublished documents from [9] Hurwicz L. (1951a). The Generalised Bayes the Hurwicz archives were provided by Wendy Minimax Principle: A Criterion for Decision Williamson of the University of Minnesota. Making Under Uncertainty Cowles Commis- These archives are now housed in Duke Univer- sion Discussion Paper Statistics 355. February sity. The paper has vastly improved in exposition 8, 1951. 5available at http://icpr.itam.mx/Hurwicz/HurwiczEconometricsClassNotes1952.pdf

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[10] Hurwicz L. (1951b). Comments on Statisti- ture. RAND Research Memorandum RM-679, cal Decisions. Cowles Commission Discussion September 4, 1951. Paper Statistics 369. November 29, 1951. [13] Savage, L. J. (1951). The Theory of Statisti- [11] Hurwicz L. (1952). Econometrics Class cal Decision. Journal of the American Statisti- Notes. Available at: cal Association 46, 55–67. http://icpr.itam.mx/Hurwicz/ [14] Savage, L. J. (1972). The Foundations of Statis- HurwiczEconometricsClassNotes1952. tics , 2nd ed., New York: Dover. pdf. [15] Sinha, T. (2008). Being Leo Hurwicz. Banga- [12] Milnor, J. (1951). Games Against Na- lore: Cranes International.

APPLICATIONS

SOMEOFTHE What?, Why?, tional model [e.g., 3, 4, 6]. In more recent years, How?, Who? AND Where? OF increasingly prevalent multi-core CPUs in stan- GRAPHICS PROCESSING UNIT dard servers, desktops and laptops have en- COMPUTINGFOR BAYESIAN gendered some interest in relatively simple and ANALYSIS easy multi-threading of existing Bayesian analysis code, whether implemented in low level lan- guages (C/C++) or through parallelisation facil- Marc A. Suchard ities in environments such as R and Matlab R . Departments of Biomathemathics, Human Genetics Much progress in research and in advancing the and Biostatistics use of Bayesian methods in increasingly compu- University of California, Los Angeles tationally challenging problems has resulted. As [email protected] we look ahead, however, the potential impact Chris Holmes of parallel computation on both immediate research and the development of more broadly use- Oxford Center for Gene Function ful software is clearly – to some of us – dramati- University of Oxford cally enhanced by the advent of scientific compu- [email protected] tation using desktop and laptop graphical pro- & cessing units (GPUs). Major new opportunities Mike West for orders-of-magnitude speed-up in computa- Department of Statistical Science tion are emerging through GPU programming, Duke University and the technology is cheap, both to purchase [email protected] and run, and easily available. We have been exploring these opportunities and developing a base of experience and examples in Bayesian analysis that bear out this “op- Over the last 20 years or so, a number of Bayesian portunistic” view; each of us is now firmly com- researchers and groups have invested a good mitted to exploiting GPU computation as a norm deal of time, effort and money in parallel com- in our research. Current directions for technolog- puting for Bayesian analysis. The growth of ical developments include emerging-technology “small research group” to “institutionally sup- GPUs that are squarely aimed at the scientific ported” cluster computational facilities has had computing community, clusters of GPUs, and in- a substantial impact on a number of areas of tegration of GPU and CPU processing in increas- Bayesian analysis, enabling analyses that are oth- ingly nimble commodity machines that enable erwise practically infeasible. Parallel computing massive parallelisation on the desktop. This will has also motivated new approaches to simula- be a big part of the compute environment for us tion and optimisation-based Bayesian computa- all in a short few years, and it seems clear (again tions that aim to maximally exploit the “master- to us!) that this technology promises to impact slave” and “embarrassingly parallel” computa-

Content 12 www.bayesian.org ISBA Bulletin, 17(1), March 2010 APPLICATIONS far more profoundly on statistical computation computational uses in addition to graphics. and software development than cluster facilities for parallelisation ever have or are ever likely to. Why? Some of these experiences and examples may be of broader interest to the Bayesian communi- For scientific computing, GPU utility emerges ties and ISBA members, in particular. when computations are inherently “massively parallel,” i.e., the computation can exploit par- What? allelization across many (hundreds or thousands of) GPU cores simultaneously. This structure GPUs are dedicated numerical processors de- emerges in many statistical models in Bayesian signed for rendering 3-dimensional computer analysis, while in others we may capitalize on graphics. They are the graphics card “engines” GPU architecture with appropriately restyled in high-end graphics computers and gaming ma- computational strategies. Among our own in- chines. In essence, a GPU consists of hundreds terests has been developing effective code for of processor cores on a single chip, and each core Bayesian mixture models for data in several tens can be programmed to apply the same numeri- of dimensions, with hundreds of mixture com- cal operations simultaneously to each element of ponents and with large data sets – millions to large data arrays – the so-called single instruc- tens of millions of observations. In such con- tion, multiple data (SIMD) paradigm. Since the texts, MCMC or posterior mode search compu- same operations (called “kernels”) function si- tations are intensive, but massively dominated multaneously, GPUs can achieve extremely high by the within-iterate (whether MCMC or EM, or arithmetic intensity so long as we can enable suf- other) calculations. In these “moderate-to-large p, ficiently fast and efficient transfer of required in- large k, very large n” problems, massive fragmen- put data “onto” the processers and, correspond- tation of calculations induced by conditional in- ingly, of the ouput data “off” the processors. dependencies are ideally suited to GPU paral- As an extension to common programming lan- lelization. GPU machines have potential to de- guages, CUDA [7, 9] opens up the GPU to gen- fine major speed-up – on cheaply and easily ac- eral purpose computing, and the computational cessible hardware – for these computations as a power of these units has increased to the stage routine, and the potential is realised; some of our where they can process data intensive problems recent examples show that first-version imple- many orders of magnitude faster than conven- mentations of MCMC and Bayesian EM in stan- tional CPUs. The development of open-source dard Bayesian mixture models enables scale-ups libraries (OpenCL: www.khronos.org/opencl) is ad- on desktop personal computers that are simply vancing, and in the coming year or two can be not achievable using multi-threaded CPU desk- expected to simply mushroom as broader ranges tops and simply impractical across distributed- of computational scientists press for, and them- memory computing clusters. Scale-ups of 100- selves develop, supporting software tools. fold in raw processing time are dramatic in terms GPUs are graphics processing work-horses of the ability to run analyses routinely, and – as in many standard desktop and laptop comput- this typical benchmark uses just first-generation ers, as well as high-end graphical workstations. GPUs and supporting software tools – this is just Among manufacturers, the NVIDIA corporation the start. Recent advanced Monte-Carlo methods is way ahead in technology and in addressing such as population-MCMC, SMC samplers and the increasing interest for scientific computa- particle-MCMC [e.g. 1] are naturally aligned to tion. The current NVIDIA GPUs include GTX GPU computation, and effective parallel imple- and Tesla varieties; these are inexpensive, com- mentations allow us to realize their advantages modity parallel machines that can be installed – in terms of increased mixing and exploration of singly or in small multiples – in many desktops high-dimensional and complex target densities and laptops, as well as in small cluster arrange- for little overheard. ments. NVIDIA’s next-generation (2010 release Novel, GPU-oriented approaches to modifying expected) Fermi GPU promises substantial in- existing algorithms and software design not only creases in numbers of cores, in processing speed provide the opportunity for vast speed-up, how- per core, in on-card memory shared by the hun- ever; critically, they also enable statistical anal- dreds of cores for fast data access, input and out- yses that presently will simply not be consid- put, as well being more heavily targeted towards ered due to compute time and other limitations

Content 13 www.bayesian.org ISBA Bulletin, 17(1), March 2010 APPLICATIONS in traditional computational environments. In spectives and strategy for algorithm implemen- one of our motivating application areas for “mas- tation, and can rely on the already established sive mixtures”, that of routine analyses of many, base of experience in a number of groups. The very large data sets in experimental biology stud- required investment in developing programming ies [2], laboratory culture is hugely resistant to skills certainly challenges researchers for whom the notion of accessing institutional clusters – for low-level programming has never been a focus, reasons of cost and access, and also due to the However, for researchers and statistical program- norms and established practice of “computing in mers aiming to transform the efficiency, poten- the lab.” Software for GPU-enabled desktops will tial impact and broader use of Bayesian models provide the opportunity for complex, practically and methods, the investment will be extremely relevant Bayesian analyses to move more aggres- worthwhile. As a rough guide we estimate that a sively into practice as a result. programmer proficient in a language such as C or C++ should be comfortable with programming How? in CUDA within around 4 weeks. Our own groups have defined a base of experi- GPU programming is fundamentally an exercise ences that others may find useful – both as entry in parallel programming. As such, key concepts points for perspective, and possibly also in terms include those of clearly and explicitly identify- of access to existing code and examples. For ex- ing the major, core compute demands of any spe- ample, we have defined some initial code and cific model analysis, and the inherent “bottle- manuscripts with overtly “tutorial” flavour, fo- necks” that limit the ability to achieve efficiencies cusing on some more-or-less standard Bayesian via parallelization. MCMC algorithms, for ex- model contexts that will be of broad use and ap- ample, are intrinsically serial algorithms, but can peal. We have developed these to show the flow still benefit (potentially massively in large-scale, of the analyses so as to engage researchers that highly structured problems) from GPU paralleli- may be interested in developing in this direction sation if the “per iterate” computations can be in related or other classes of statistical models. parallelised. That GPU cores share memory on the unit means that data stored “locally” can be Who & Where? quickly and efficiently accessed, so consideration must also be given to the basic programming is- Some links to groups involved in GPU computa- sues of simply moving data around. tion for statistical research and application gen- For NVIDIA GPUs, CUDA is a parallel erally, as well as specific groups and projects in computing technology, and programming lan- Bayesian analysis that provide resources – pa- guage, that enables access to GPU comput- pers, examples, software – include those noted ing via modifications of standard computing and linked below, among others. The current (in C/C++). OpenCL is an emerging li- authors are committed to working towards the brary that provides access to GPUs from sev- merging of their own sites to provide a central eral hardware providers. Both require low- resource for the field. level programming for which researchers new to GPU programming should develop basic fa- • www.stat.duke.edu/gupstatsci cility. On the near horizon stand higher-level, Massively parallel GPU-based computing flexible interfaces for GPU programming, such for statistical science, and Bayesian anal- as Thrust (code.google.com/p/thrust) that provides ysis, at Duke University, headed by Mike many standard parallel algorithms in an easier- West. This site links to articles and software to-use form than CUDA. We currently recom- with a focus on GPU in Bayesian analysis mend prototyping using Thrust and then re- broadly. Readers can find there the tutorial- implementing critical code parts in CUDA for level “How to?” material, as well as code, raw speed and performance. for efficient GPU analysis of Bayesian mix- To capitalise on the opportunities for Bayesian ture models described in [12]. The site is computations that are offered by GPUs – in the developing to include additional GPU soft- near term – requires some investment of time and ware for a range of complex Bayesian mod- effort (though limited money!) to adapt standard els (e.g., for the large-scale, spatial (and 3D code to the GPU environment. This involves spatio-temporal) models of [5]) and to add relatively modest changes in programming per- links and resources of broader interest to

Content 14 www.bayesian.org ISBA Bulletin, 17(1), March 2010 REFERENCES

the Bayesian community. is a CUDA library of parallel algorithms with a high-level interface to enhance de- • www.oxford-man.ox.ac.uk/gpuss/ veloper productivity. Bayesian GPUSS, the GPU stochastic simulation group at Oxford University, headed L by Chris Holmes. Readers can find links to current research papers and online resources as well as a series of tutorial pa- References pers and coded examples, including the overview paper on advanced Monte Carlo [1] Andrieu, C., Doucet, A. and Holenstein. R. methods for Bayesian inference [8]. The site (2010). Particle Markov Chain Monte Carlo aims to maintain a list of papers published (with discussion). J. Royal Statistical Soc. B, in the field relevant to statistical computa- (to appear). tion using GPUs. [2] Chan, C., Feng, F., West, M. and Kepler, T.K. • www.biomath.ucla.edu/msuchard/ (2008). Statistical mixture modelling for Marc Suchard’s group at UCLA. This site cell subtype identification in flow cytome- provides access to some of the first detailed try. Cytometry, A, 73:693–701. GPU work in Bayesian analysis in challeng- [3] Hans, C., Dobra A. and West, M. (2007). ing problems in computational biology and Shotgun stochastic search in regression with high-dimensional optimization [10, 11, 14]. many predictors. Journal of the American Sta- • brainarray.mbni.med.umich.edu/ tistical Association, 102:507–516. Brainarray/rgpgpu/: [4] Hans, C., Wang, Q., Dobra, A. and West, M. + R GPU. This R package off-loads several (2007). SSS: High-dimensional Bayesian re- common data-summary tools from R to the gression model search. Bulletin of the Inter- GPU. national Society for Bayesian Analysis, 24:8–9. • www.stat.psu.edu/~mharan/ [5] Ji, C., Merl, D., Kepler, T.B. and West, W. Murali Haran’s group at PSU. This site pro- (2009). Spatial mixture modelling for unob- vides a GPU example involving slice sam- served point processes: Application to im- pling [13]. munofluorescence histology. Bayesian Anal- • gpgpu.org/ ysis, 4:297–316. The community site, resource and net- [6] Jones, B., Dobra, A., Carvalho, C.M., working arena for researchers interested in Hans, C., Carter, C. and West M. (2005). General-Purpose computation on Graphics Pro- Experiments in stochastic computation for cessing Units. high-dimensional graphical models. Statis- tical Science • www.nvidia.com/page/home.html , 20:388–400. www.nvidia.com/object/cuda_home_new. [7] Kirk, D. and Hwu W. (2009). Programming html Massively Parallel Processors: A Hands-on Ap- The NVIDIA and NVIDIA/CUDA site for proach. Morgan-Kaufman. CUDA progamming of GPUs; keep up with the latest technology and software [8] Lee, A., Yan, C., Giles, M.B., Doucet, A. advances, and access scientific computing and Holmes C.C. (2009). On the util- networks. ity of graphics cards to perform massively parallel simulation of advanced • www.khronos.org/news/C124/ Monte Carlo methods. Technical report, The Kronos Group web site with informa- http://arxiv.org/abs/0905.2441. tion and resources related to the OpenCL library that brings general purpose GPU pro- [9] NVIDIA-CUDA. (2008). Nvidia cuda gramming to a variety of hardware plat- compute unified device architec- forms. ture: Programming guide version 2.0. http://developer.download.nvidia. • code.google.com/p/thrust/ com/compute/cuda/2_0/docs/NVIDIA_ Thrust, Code at the Speed of Light. Thrust CUDA_Programming_Guide_2.0.pdf

Content 15 www.bayesian.org ISBA Bulletin, 17(1), March 2010 SOFTWARE HIGHLIGHT

[10] Suchard, M.A. and Rambaut, A. (2009). sively parallel massive mixtures. Journal BEAGLE: broad-Platform Evolutionary of Computational and Graphical Statistics. (to Analysis General Likelihood Evaluator. appear). http://beagle-lib.googlecode.com. [13] Tibbits, M.M., Haran, M. and Liechty, J.C. [11] Suchard, M.A. and Rambaut, A. (2009). (2009). Parallel multivariate slice sampling. Many-core algorithms for statistical phylo- Technical report, Department of Statistics, genetics. Bioinformatics, 25:1370–1376. PSU. [12] Suchard, M.A., Wang, Q., Chan, C., [14] Zhou, H., Lange, K.L. and Suchard, M.A. Frelinger, J., Cron, A. and West, M. (2010). (2009). Graphical processing units and high- Understanding GPU programming for dimensional optimization. Technical report, statistical computation: Studies in mas- Department of Human Genetics, UCLA.

SOFTWARE HIGHLIGHT

BAYESIAN FUNCTIONAL DATA set of inferential tools for data where some or ANALYSIS USING WINBUGS all variables are functions. Functional principal component analysis (FPCA) is one of the main techniques for functional data compres- Ciprian M. Crainiceanu sion. FPCA has been extended to the multi- Department of Biostatistics level case [3, 5] and to multilevel functional re- Johns Hopkins University gression [2, 4]. The success of these approaches [email protected] is essentially based on: 1) the massive amounts of compression achieved by PCA; 2) the ﬂexible Modern observational and experimental biolog- mixed effects framework that allows simple gen- ical data has undergone a revolution. Driven eralizations and adaptation of methods; and 3) by new biotechnology and computing advances, the Bayesian and frequentist computational ad- high dimensional, high density, functional mul- vancements over the last 15 − 20 years. tilevel and longitudinal biological signals are Our paper [1] presents a compilation of becoming commonplace in medical and public Bayesian FDA analyses implemented in Win- health research. These types of signals histori- BUGS. Examples start from standard models and cally occurred in small clinical or experimental build incrementally more complexity to models settings, often referred to as the “small n, large that are not yet implemented in any other soft- p” problem. The extension of these biological sig- ware; see, for example, the section on functional nals to cohort studies with longitudinal or hierar- regression using penalized B-splines. The most chical structure is the next generation of Biosta- important contribution of our software is to pro- tistical problems. We have taken to calling this vide a glimpse into the enormous potential of the “hierarchical large n, large p” problem. A Bayesian computational methods applied to the now-standard example of this type of data is ob- emerging problems raised by new types of obser- servational studies containing images or biosig- vational studies. Accompanying software can be nals, such as Electroencephalograms (EEG) or downloaded for free from the Journal of Statisti- Electrocardiograms (ECG), on thousands of sub- cal Software website jects over time. Our research group is currently http://www.jstatsoft.org/v32/i11 working on 6 studies of this type with a total of more than 30 Terabytes (Tb) of data. These new and complex data have led to a Models considered resurgence of interest in powerful techniques The software allows to specify a wide range of like the principal component analysis, singular exposure and regression models. value decomposition, multilevel models, mixed models and Bayesian methods. Functional Data • Functional principal component analysis Analysis (FDA) [6] is a particularly powerful • Functional regression models

Content 16 www.bayesian.org ISBA Bulletin, 17(1), March 2010 REFERENCES

– Classical functional regression The WinBUGS code for this model is: – Functional penalized regression – Regression with functional scores as out- {model comes {for (i in 1:N_subj) • Functional multilevel models {for (t in 1:N_obs) {W[i,t]~dnorm(m[i,t],taueps) The excellent properties of Bayesian analysis in m[i,t]<-inprod(xi[i,],psi[t,])} this context are due to: 1) low dimensional pro- for (k in 1:dim.space) jection bases; 2) mixed model representation; and {xi[i,k]~dnorm(0,ll[k])} 3) modularity and ﬂexibility. }#End for i

A simple example for (k in 1:dim.space) {ll[k]~dgamma(1.0E-3,1.0E-3) Consider 500 time series, W (t), representing the i lambda[k]<-1/ll[i]} observed EEG fraction of δ-power, for subject i = taueps~dgamma(1.0E-3,1.0E-3) 1,...,I = 500, recorded for 1 hour after sleep on- }#End model set at the 30-second interval t = 1,...,T = 120; for a detailed description see [2, 3]. After subtract- Here W[i,t] is the observed percent δ-power, ing the population mean from W (t), we assume i W (t), xi[i,] is the vector of scores, ξ , psi[t,] that W (t) = X (t) + (t), where X (t) is the true i ik i i i i is the vector of eigenfunctions, ψ (t), evaluated fraction of δ-power. By using the spectral decom- k at t, ll[k] is the precision τ = 1/λ controling position of the estimated covariance operator of k k the amount of shrinkage of scores ξ , i = 1,...,I. X (t) and by retaining the first 10 eigenfunctions, ik i We obtained 1500 simulations, discarded the first ψ (t), k = 1,..., 10, the model becomes k 500 as burn-in and used the remainder 1000 for ( PK I = 500 T = 120 Wi(t) = k=1 ξikψk(t) + i(t); inference. For subjects and grid i.i.d. i.i.d. 2 points the total computation time was 4.8 min- ξik ∼ N(0, λk); i(t) ∼ N(0, σ ), utes (Dual Core Processor 3GHz, 8Mb RAM PC). which is a mixed effects model with normally This number of simulations was enough for our distributed principal component scores, ξik. This purposes because convergence and mixing of the is not a restriction and other distributions can chains was excellent. Figure 1 shows the poste- be considered with minimal changes to the soft- rior mean δ-power and pointwise 95% credible ware. We use the following priors for the pre- intervals for four subjects for the first hour after 2 cision parameters 1/λk, 1/σ ∼ Γ(0.001, 0.001). sleep onset.L

References cipal Component Analysis. Annals of Applied Statistics, 3: 458-488. [1] Crainiceanu, C.M., Goldsmith, A.- J. (2009) Bayesian Functional [4] Goldsmith, A.-J., Feder J., Crainiceanu Data Analysis using WinBUGS. C.M., Caffo B.S., Reich D. (2009) http://www.jstatsoft.org/v32/i11 Jour- Penalized Functional Regression. nal of Statistical Software, 32(11) http://www.bepress.com/jhubiostat/paper204/ [5] Staicu, A.-M., Crainiceanu, C. M., Carroll, R. [2] Crainiceanu, C.M., Staicu, A.-M., Di, C. J., (2010) Fast Methods for Spatially Corre- (2009) Generalized Multilevel Functional Re- lated Multilevel Functional Data. Biostatistics, gression. Journal of the American Statistical As- Advanced access January, 2010. sociation, 104(488): 1550-1561. [6] Ramsay, J.O. and Silverman, B.W. (2006) [3] Di, C., Crainiceanu, C.M., Caffo, B.S., Pun- Functional Data Analysis. Springer-Verlag, jabi, N.M. (2009) Multilevel Functional Prin- New York.

Content 17 www.bayesian.org ISBA Bulletin, 17(1), March 2010 STUDENTS’ CORNER

● ● ● ●● ● ● ● ●● ● ● ● ● ● ● ● ● ●●● ● ● ● ● ● ● ● ● ● ●●● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● 0.8 ● ● 0.8 ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ●●●

0.7 0.7 ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ●●● ● ●● ● ● ●● ● ●● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ●● ● ● ●

0.6 ● 0.6

power ●● ● power ● ● ● ● ● ● δ δ ● ●● ● ● ● ● ● % % ● 0.5 ● 0.5 ● ● ● ● 0.4 0.4

0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1

Time (hours) ● Time (hours)

●

● ● ● ●

● ● ● 0.8 ● ● ● ● 0.8 ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● 0.7 ● ● ● ● 0.7 ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 0.6 ● ● 0.6 ● ●

power ● power ● ● ●● ● ● ● ● ● ●●

δ ● δ ● ● ● ● ● ● ● % % ● ● ● 0.5 0.5

● ●

● 0.4 0.4

0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1

Time (hours) Time (hours)

Figure 1: Data for ﬁrst hour from sleep onset (black dots), posterior mean (black line) and 95% pointwise credible intervals for 4 subjects.

STUDENTS’ CORNER

CALLFOR DISSERTATION stract will not only provide exposure for your re- ABSTRACTS search, but it may potentially lead to collabora- tions with future colleagues. In addition, you are Luke Bornn providing an important service to the Bayesian [email protected] community by giving established researchers a Recent Ph.D graduates, having your dissertation taste of the interests of young researchers. Fac- abstract published is as simple as emailing it to ulty, please encourage your students’ participa- the email address above. Publishing your ab- tion.L

NEWS FROM THE WORLD

CALLFOR ANNOUNCEMENTS Meetings and conferences

Sebastien Haneuse 10th Bayesian Statistics Brazilian Meeting, [email protected] Green Coast, Brazil. 21-24th March, 2010. The 10th EBEB will take place at Portogalo I would like to encourage those who have any Suites Hotel, located in the pleasant Green Coast announcements or would like to draw attention area of the State of Rio de Janeiro, Brazil. It is to an up-coming conference, to get in touch with about 150km far from the city of Rio de Janeiro. me and I would be happy to place them here. In this 10th edition, we aim to discuss recent developments in the area both from the methodological and computational points of view. These developments will be presented and discussed

Content 18 www.bayesian.org ISBA Bulletin, 17(1), March 2010 NEWS FROM THE WORLD by leading researchers in the world with a short Short courses and workshops course, 13 plenary talks, 8 oral presentations and 2 poster sessions. Since its 6th edition, EBEB is organized by ISBrA, the Brazilian chapter of ISBA, Summer Institute 2010: Workshops in Quanti- EBEB X is supported by ISBA. tative Research Methodology, Charleston, SC. 3- Submissions and registration can be made at 4th May, 2010. www.dme.ufrj.br/ebebx. The 2010 Summer Institute at the Medical Uni- versity of South Carolina (MUSC) offers 4 two- ISBA 2010 World Meeting/Ninth Valencia In- day workshops that introduce current quanti- ternational Meeting on Bayesian Statistics, tative methods in key areas of biomedical and Benidorm, Spain. 3-8th June, 2010. clinical research and offer hands on experience The ISBA 2010 World Meeting will be held with implementing these methods. The tar- in conjunction with the Ninth Valencia In- geted audience includes graduate students, res- ternational Meeting on Bayesian Statistics in idents, fellows, clinical researchers, biostatisti- Benidorm, Spain. As already announced in Va- cians, biomedical researchers and epidemiolo- lencia 8, this will be the last Valencia meeting per- gists. sonally organized by Jose´ M. Bernardo (who will The Bayesian Biostatistics course is intended be 60 when the conference takes place). After Va- to provide a basic introduction to the principles lencia 9, the Valencia meetings will become reg- and use of Bayesian methods in biostatistics. Day ular ISBA World Meetings (which will not neces- 1 will be an introduction to Bayesian hierarchi- sarily take place in the State of Valencia). ISBA cal modeling and to the use of Winbugs. Day world meetings will therefore take place every 2 features hands on by the participant and will two years. The meeting will be structured in tuto- cover a series of topics and particular interest in rials on the first day, contributed talks in the late biostatistics applications including longitudinal afternoons, and poster sessions in the evenings. analysis, missing data methods, survival analy- Additional information can be found at http: sis and measurement error modeling. //www.uv.es/valenciameeting. More information can be found at http:// academicdepartments.musc.edu/dbe. CBMS Regional Conference - Bayesian Non- parametric Statistical Methods: Theory and Bayesian Econometrics - A Short Course, Wash- Applications, Santa Cruz, CA. 16-20th August, ington, DC. 24-28th May, 2010. 2010. The Info-Metrics Institute and the Department Bayesian nonparametric (BNP) methods com- of Economics of American University, Washing- bine the advantages of Bayesian modeling (e.g., ton, DC, are pleased to announce two upcoming ability to incorporate prior information, full and summer program courses, “Bayesian Economet- exact inference, ready extensions to hierarchical rics & Decision-Making” with John Geweke, U settings) with the appeal of nonparametric in- Iowa and UTS, Australia. . The primary pur- ference. In particular, they provide data-driven, pose of the summer program in applied econo- albeit model-based, inference and, importantly, metrics is to provide students, researchers and more reliable predictions than parametric mod- faculty with state of the art econometric methods els. for analyzing data in the Social Sciences. Each Theoretical research on BNP methods and their day of the week-long course consists of morn- applications has grown dramatically in the last ing lectures that develop the basic concepts and fifteen years. This has produced a massive body philosophy as well as their applications to real of scattered literature, which can be daunting for economic problems and data. Each afternoon, newcomers and hard to follow even for special- these methods will be applied and practiced in ists. This CBMS conference, to be held between the computer lab. These daily tutorials and work August 16th and August 20th, 2010, aims at pro- in the computer lab provide students with ‘hands viding a comprehensive introduction to the field on’ experience in using these methods with real for new researchers, and in particular graduate data. students postdocs and junior researchers. More information can be found at Additional information can be found at http: http://www.american.edu/cas/economics/ //www.ams.ucsc.edu/CBMS-NPBayes. info-metrics/econometrics.cfm.

Content 19 www.bayesian.org ISBA Bulletin, 17(1), March 2010 NEWS FROM THE WORLD

Advanced Bayesian Disease Mapping, ence for PK and PD as an important motivating Charleston, SC. 3-4th June, 2010. application area of non-parametric Bayes. This course is designed to provide advanced The program will begin with a week of tuto- coverage of Bayesian disease mapping topics in rials and workshop activities. There will be ex- applications to Public Health and Epidemiology. tended, tutorial-style talks during morning ses- Emphasis on the course is placed on spatial and sions, and contributed and invited research talks spatio-temporal Bayesian modeling issues, and during the afternoons. Afternoon talks will be se- some knowledge of Bayesian computation and lected to complement topics covered in the morn- WinBUGS is assumed. ing sessions. At the end of the first week work- More information can be found at http:// shop research working groups will be formed. academicdepartments.musc.edu/dbe. The working groups will tackle particular research problems in the area. Working group activities can include workshop-style presentations Carlo Alberto Stochastics Workshop, Turin, by group members to stimulate discussion on Italy. 11th June, 2010. specific issues The theme of the workshop is Bayesian asymp- A detailed description of activities, along totics and the meeting aims at presenting some with application information is avail- of the latest advances on asymptotics of Bayesian able at http://www.samsi.info/programs/ infinite-dimensional models. The increasing use 2010bayes-summer-program.shtml. of Bayesian nonparametric models in statistical practice has stimulated a very active area of re- 8th Workshop on Bayesian Nonparametrics, Ve- search which analyses their large sample proper- racruz, Mexico. 26-30 June, 2011. ties according to frequentist criteria. Indeed, in The workshop aims at presenting the lat- the last decade there has been a wealth of results est developments on Bayesian nonparametric establishing convergence of the posterior distri- statistics, covering a wide range of theoretical, bution to the “true” distribution that has gener- methodological and applied areas. The work- ated the data and the speed with which such a shop will feature tutorials on hot topics, invited convergence is achieved. Moreover, also other and contributed talks and poster sessions. different approaches to study asymptotic proper- Scientific committee: David B. Dunson, Sub- ties of Bayesian models have been pursued lead- hashis Ghosal, Jim Griffin, Nils L. Hjort, Michael ing to interesting and important results. This I. Jordan, Yongdai Kim, Antonio Lijoi, Ramses meeting will feature invited talks delivered by H. Mena, Peter Mueller, Luis E. Nieto, Igor Pru- some of the scholars who have been contributing enster, Fernando A. Quintana, Yee W. Teh and to the field in recent years. Stephen G. Walker. It will be held at the Collegio Carlo Alberto, a Research Institution housed in an historical building located in Moncalieri on the outskirts of Turin, Italy. Open Positions More information can be found at www. carloalberto.org/stats_workshop. 1. University of Connecticut The University of Connecticut Department of 2010 Summer Program on Semiparametric Statistics at Storrs invites applications for tenure Bayesian Inference: Applications in Pharma- track assistant professor in Environmental / Spa- cokinetics and Pharmacodynamics, Research tial Statistics, beginning August, 2010. Triangle Park, North Carolina. 12-23rd July, 2010. Responsibilities will include methodological and collaborative research in environmental and The purpose of this program is to bring to- spatial statistics, teaching at both graduate and gether a mix of experts in pharmacokinetics (PK) undergraduate levels, and supervision of stu- and pharmacodynamics (PD) modeling, non- dents. parametric Bayesian inference, and computation. Candidates are expected to hold a doctoral de- The aims of the program and workshop are (i) to gree in Statistics or related fields. Equivalent for- identify the critical new developments of infer- eign degrees are acceptable. The new faculty ence methods for PK and PD data; (ii) to deter- is expected to demonstrate excellence in all the mine open challenges; and (iii) to establish infer- above referenced activities. Strong interpersonal

Content 20 www.bayesian.org ISBA Bulletin, 17(1), March 2010 NEWS FROM THE WORLD and communication skill is preferred. Incum- tics Core that will facilitate the proposed growth bent may be required to work at the University of Clinical and Translational Science across the of ConnecticutOs˜ main campus located in Storrs, CICATS Consortium. In addition to his/her and/or the campuses at Avery Point, Hartford, own original research and research collabora- Stamford, Torrington, Waterbury, and West Hart- tions, he/she will be responsible for the opera- ford. Salary is competitive based on experience tions of the Research Design, Epidemiology and and qualifications. Biostatistics core. CICATS investigators will in- Applicants must send a cover letter, curricu- clude trainees and both junior and senior faculty lum vita, statements of research and teach- members from multiple disciplines. The faculty, ing interests, copy of transcript, and three in collaboration with a team of epidemiologists letters of reference in pdf files by e-mail to and masterOs˜ level staff, will provide guidance [email protected] or by regular mail to Dr. to transdisciplinary teams for the development Ming-Hui Chen, Department of Statistics Uni- of research studies. He/she will also be respon- versity of Connecticut , 215 Glenbrook Road, U- sible for biostatistical teaching in the new Master 4120, Storrs, CT 06269-4120 Inquiries should be of Science in Clinical and Translational Research. addressed to Ming-Hui Chen, search committee The candidate must hold a doctorate in bio- chair at mhchen at [email protected] (Search 2010 statistics or a closely related discipline and 220) demonstrate past success with self-initiated research, extramural funding and published schol- 2. University of Connecticut arship, the ability to work in collaboration with The Department of Statistics at the University clinical and/or basic scientists. The candi- of Connecticut invites nominations and applica- date must contribute through research, teaching, tions for one full time position in the Biostatistics and/or public engagement to the diversity and core of the Connecticut Institute of Clinical and excellence of the learning experience. Translational Science (CICATS). This position is Curriculum vitae and a cover letter sent to the a full-time, tenure track position at any level. Chair search committee, Department of Statis- This biostatistician faculty member will have tics, University of Connecticut. We request that an appointment within the Department of Statis- the application materials in pdf files to be sent tics at the UConn Storrs Campus, but will have through e-mail to [email protected] L major responsibility for the CICATS Biostatis-

Content 21 www.bayesian.org ISBA Bulletin, 17(1), March 2010

Executive Committee Board Members:

President: Peter Muller¨ 2010–2012: Past President: Mike West Sidhartha Chib, Arnaud Doucet, Peter Hoff, Raquel Prado President Elect: Michael I. Jordan Treasurer: Gabriel Huerta 2009–2011: Executive Secretary: Merlise Clyde David Dunson, David van Dyk, Katja Ickstadt, Brunero Liseo Program Council 2008–2010: Sylvia Fruhwirth-Schnatter,¨ Lurdes Inoue, Hedibert Lopes, Sonia Petrone Chair: Alex Schmidt Vice Chair: Igor Pruenster¨ Past Chair: Herbie Lee

EDITORIAL BOARD

Editor

Manuel Mendoza [email protected]

Associate Editors

Interviews Bayesian History Donatello Telesca Tim Johnson [email protected] [email protected] www.sph.umich.edu/iscr/faculty/ Annotated Bibliography profile.cfm?uniqname=tdjtdj Beatrix Jones [email protected] Students’ Corner www.massey.ac.nz/∼mbjones/ Luke Bornn [email protected] Software Highlight www.stat.ubc.ca/∼l.bornn/ Alex Lewin [email protected] News from the World www.bgx.org.uk/alex/ Sebastien Haneuse [email protected] http://www.centerforhealthstudies.org/ ctrstaff/haneuse.html

Content 22 www.bayesian.org