September 2005 the Oﬃcial Bulletin of the International Society for Bayesian Analysis

THE ISBA BULLETIN

Vol. 12 No. 3 September 2005 The oﬃcial bulletin of the International Society for Bayesian Analysis

AMESSAGEFROMTHE PRESIDENT his editorial board for all the work that they have put in on this venture and congratulate them on by Sylvia Richardson having produced such an exciting issue. It is now ISBA President up to all ISBA members and the Bayesian commu- [email protected] nity at large to help sustain the journal by submit- ting their recent work for publication in our jour- I hope that you all have had a productive break nal. making full use of the conference season to spring towards new statistical challenges. It is remark- AMESSAGEFROMTHE EDITOR able to see how, nowadays, the Bayesian ideas are intertwined in so many sessions at the major sta- by J. Andr´esChristen tistical conferences. We must carry on striving to [email protected] continue to create links with other societies and interest groups and the recent creation of ISBA This issue of the ISBA Bulletin is specially varied sections is a step in this direction. Preparation with several interesting columns to read. Of spe- for a high point in our calendar, the joint Valen- cial interest for ISBA members are the ISBA Elec- cia/ISBA meeting in 2006 is well under way and tions section and the Valencia/ISBA call for Oral the ISBA programme committee chaired by Kerrie Presentations. Also, the Bulletin web page is up Mengersen is now calling for oral contributions. I again with all 2004 issues available: http://www. am sure that all of you are looking forward to par- cimat.mx/∼jac/ISBABULLETIN. I hope you enjoy ticipate in our next conference and that we can an- reading this issue of the ISBA Bulletin. ticipate a record number of abstracts being submit- Contents ted! ' $ While travelling over the summer, some ® ISBA Elections Bayesian fellows visiting London made a pilgrim- Page 2 age to the Reverend Bayess grave at Bunhill Fields. They found that the grave has deteriorated, is at ® VALENCIA/ISBA INFORMA- risk of collapsing and that the Reverend Bayess TION name is not clearly visible. The maintenance on Page 6 the grave was last carried out in 1999 thanks to the personal effort of Tony OHagan. It is now becom- ® BAYESIAN HISTORY ing urgent to organise new repairs and to envisage Page 6 a solution towards a regular upkeep. I will keep ® ANNOTATED you posted on developments and ideas on how the BIBLIOGRAPHY society can be involved. I would like to thank Dale Page 9 Poirier and Lisa Tole for their keen interest and ﬁnding out useful contacts with the city of London ® STUDENT CORNER historic buildings department. Page 14 The last month has seen the remarkable achieve- ment of the publication of our new electronic jour- ® NEWS FROM THE WORLD nal Bayesian Analysis. I must thank Rob Kass and Page 15

& % SUGGESTIONS PLEASE, FEELCOMPLETELYFREETOSENDUSSUGGESTIONSTHATMIGHT IMPROVETHEQUALITYOFTHEBULLETIN [email protected] ISBA Bulletin, 12(3), September 2005 ISBA ELECTIONS

THISYEAR ELECTIONS President Elect Nominees by Jim Berger [email protected] Peter Green The 2005 elections of future ISBA officers will Affiliation and current status: Professor of Statis- take place electronically at the ISBA web-site tics, and Henry Overton Wills Professor of Math- (http://www.bayesian.org/election/voter. ematics, University of Bristol, UK. Web page and html) from October 15 through November 15. In- email address: http://www.stats.bris.ac.uk/ structions for voting will be emailed to all current ∼peter; [email protected]. ISBA members prior to the election. I am delighted Areas of interest: Bayesian computation and to announce that the 2005 Nominations Commit- MCMC, graphical models, spatial statistics, mix- tee has assembled a remarkable slate of candidates tures and hidden Markov models, gene expression for the election. In alphabetical order by office, the modelling, applications in physical sciences. 2005 candidates are: Honours: Fellow of the Royal Society, 2003; Fel- For President Elect: low of IMS, 1991; Royal Statistical Society Guy • Peter Green (UK) medals in Silver (2001) and Bronze (1987). ISI Highly-cited Researcher (author #4 mathematical • Rob Kass (USA) science paper, 1995-2005). Journals and books: JRSS(B), JASA, Biometrika, For Board Membership: Scandinavian Journal of Statistics, Journal of Com- • Marilena Barbieri (Italy) putational and Graphical Statistics, Highly Struc- tured Stochastic Systems (edited jointly with N. L. • Wes Johnson (USA) Hjort and S. Richardson), Nonparametric regres- • Steve MacEachern (USA) sion and generalized linear models: a roughness penalty approach (with B. W. Silverman), Complex • Manuel Mendoza (Mexico) Stochastic Systems (ed. Barndorff-Nielsen, Cox, • Judith Rousseau (France) and Kluppelberg).¨ Previous service to ISBA: none yet, but I would • Simon Wilson (Ireland) be pleased and honoured to begin. • Brani Vidakovic (USA) Service to other Societies: Royal Statistical So- ciety (member of Council, 1986-89, Hon. Secre- • Jim Zidek (Canada) tary, 1988-94, Chair Research Section, 1996-99, Pres- Biographical information for each of the candi- ident, 2001-03); Institute of Mathematical Statis- dates appears below. The candidates for president tics (member of Council, 1998-2001); Bernoulli So- have also included statements about what they in- ciety (member of Council, 1991-96); Chair, Euro- tent to accomplish. This information is also cur- pean Science Foundation network on Highly Struc- rently accessible on the ISBA web-site. tured Stochastic Systems (1993?95); Associate Ed- The 2005 Nominations Committee was ap- itorships: Journal of the Royal Statistical Society, pointed by the ISBA Board under the direction Series B (1984-89), Journal of the American Statisti- of President Sylvia Richardson. The members cal Association (1988-93), Annals of Statistics (1995- of the Committee were Jim Berger (USA), Guido 2000), Biometrika (1998-2002, 2005-), Scandinavian Consonni (Italy), Dipak Dey (USA), Chris Holmes Journal of Statistics (1994-98). (UK), Daniel Pena˜ (Spain), Fabrizio Ruggeri (Italy), and Jon Wakefield (USA). Beginning our delibera- My view of ISBA tions in early July, we compiled a large list of potential candidates for each office. The final slate The last 15 years or so has been a great success story was then selected through rounds of approval vot- for Bayesian statistics, and ISBA has played a big ing and ranking. Because of the abundance of tal- part in this. With imaginative leadership, a strong, ent in ISBA this was a nontrivial task, and I greatly lively and truly international research community appreciate the diligence of the committee members has been built. It is time now to build on past suc- in making some tough choices. Finally, I am very cesses, to create an even livelier future for the sub- grateful to all the candidates for their willingness ject and its participants. to serve and lead ISBA. Through them the bright Members often cite the “family” qualities of future of ISBA is assured. ISBA as key to its success, and to their motivation

2 to join in its activities. It is extraordinary, and very Rob Kass rewarding, to be part of a circle of friends who may be broadly dispersed geographically but are nev- Affiliation and current status: Professor, Depart- ertheless close scientifically, easy to communicate ment of Statistics and Center for the Neural Basis with spontaneously by email, and magically there, of Cognition, Carnegie Mellon University. http: ∼ in person (eager to buy you a drink even) when //www.stat.cmu.edu/ kass; [email protected]. you check in to that hotel in Chile, or Crete, or Is- Areas of interest: Bayesian methods (duh!), tanbul, or Cape Town! This network of relation- Statistics in neuroscience; functional data analysis. ships is very special and we must preserve it. But Honors: Elected Fellow, ASA, IMS, AAAS; 3rd healthy families do not keep all their relationships most highly cited researcher in mathematical sci- “in the family” and I think we should continue to ences, 1995-2005 (Institute for Scientific Informa- strengthen our network of relationships outside the tion). Bayesian community. We should do so for both “in- Previous service to ISBA: Vice President, 1994- ward” and “outward” reasons: to enliven our own 1996; Board of Directors, 1998-2000; Founding debates by input from other communities –both of Editor-in-Chief of Bayesian Analysis (2004-2006). statisticians and other researchers– and to give our- Service to other societies: U.S. National selves new channels for extending the reach and in- Academy of Sciences, Board of Mathematical Sci- fluence of Bayesian ideas into other disciplines. ences and its Applications, 2003-2005; U.S. Na- We probably need to have a debate about how tional Institute of Statistical Science, Board Mem- best to do this, but some steps in the right direction ber, 2004-2006; Chair-elect, Chair, Past-Chair, Sec- could be: tion on Statistics, American Association for the Advancement of Science, 2003-2006; IMS Council • Expanding the range of ISBA sections. 1999-2002; Chair-elect, Chair, Past-chair, ASA Sec- tion on Bayesian Statistical Science, 1996-1998; Ex- • Further encouragement of joint meetings ecutive Editor, Statistical Science, 1992-1994; Ed- with other societies, in statistics, in other itorial board member: Annals of Statistics, 1985; data-analytic disciplines, and in applied JASA, 1986-1992; Biometrika, 1996-2003; Statistics fields. in Medicine, 1991-1992. • Dissemination of Bayesian ideas in popular science media. My view of ISBA • More material for non-experts on the ISBA The new journal Bayesian Analysis matched its website. founding organization in both name and spirit, • Establishing “policy” working parties on hoping to reflect an outward-looking view of its major areas of statistical application where subject as something of interest not only to statisti- Bayesian approaches have been resisted (e.g. cians but to a very broad spectrum of quantitative official statistics, drug regulation?). researchers. Living up to this promise remains a major challenge to both ISBA and its fledgling jour- The other priority area I see for ISBA is ac- nal. tivity that gives further support and encourage- I am frequently struck by the remarkably wide ment to younger statisticians. They are the fu- use of Bayesian analysis in diverse scientific and ture of our discipline. What do they need? Some technological domains. ISBA should represent tried and trusted activities include the Savage both the “core” of theoretical and methodological award, student sessions and travel support at con- development, and the many disciplinary applica- ferences, tutorial sessions and summer schools. A tion areas that continue to bring fresh issues back very successful ingredient of the Highly Structured to the core. Many ISBA members sit at the inter- Stochastic Systems programme in Europe in the face with a favorite area, and some identify them- 90’s was the system supporting individual research selves strongly with these. While there have been visits, which was biased towards younger partici- some commendable efforts to establish firm cross- pants. ISBA does not have the resources to replicate disciplinary connections, it seems to me that our this, but it could sponsor applications to funding professional society must try to do more in this di- agencies that do. I don’t know what else younger rection. There is likely much to be gained by addi- researchers need, let’s ask them! tional communication and collaboration. And on the subject of grass-roots participation What should ISBA do? I would suggest and empowerment, are we doing enough to help first gathering some information on existing all our members participate in deciding where application-area involvement of ISBA members, in- ISBA goes and what it does? cluding an assessment of current status and need

3 for more formal involvement of ISBA through both Society in 1996. She has served on the ISBA Nom- meetings and publications. There is probably a lot ination committee and as Corresponding Editor of to be learned, and a lot to be done, even in ar- the ISBA Bulletin. eas where ISBA members participate actively. Sec- ond, it is possible to search out researchers who do Wes Johnson Bayesian analysis, yet have little interaction with those who specialize in Bayesian methodology—I I am currently a Professor of Statistics at the Uni- meet such people within my own realm of neuro- versity of California at Irvine after having recently science, and they are usually quite keen to get help moved from UC Davis. My interests are in the and to increase their own depth of knowledge. We development of non and semiparametric methods ought to be able to welcome them into the fold via in a variety of contexts including longitudinal and invitations to speak and write for us. survival data analyses, the development of practi- After retiring as department head at Carnegie cal Bayesian methods in Epidemiology, the devel- Mellon, after nine years of service, I have found opment of informative priors in general mixed re- myself thinking occasionally about where I might gression models, and in asymptotic methods. Over put some new organizational effort. Advancing the years I have published methodological papers ISBA’s cross-disciplinary presence seems to me a in JASA, Biomtrika and JRSSB. I have also had long highly worthwhile goal, and one that fits well with term collaborative arrangements with the veteri- my work organizing the Case Studies in Bayesian nary and medical schools at UC Davis and these Statistics workshops (now at number 8) and the have resulted in many (Bayesian) papers that are Statistical Analysis of Neuronal Data workshops published in subject matter journals as well as in (now at number 3). One particular point is that Biometrics, Statistics in Medicine and Biostatistics. I would like to see ISBA play a formal role in the Over the years I have primarily contributed ef- Case Studies workshops (and maybe the Neuronal forts to SBSS, but recently I was the chair of the workshops too). In addition, we can and should Savage Trust Committee, I was also a member of right away begin trying to have Bayesian Analysis the Savage Award Committee and am currently increase the breadth of its audience. I would like an Associate Editor for Bayesian Analysis. I am to mention, however, that while my work on the very pleased to be a part of a statistics community new journal has developed into a kind of labor of that actively encourages truly cooperative efforts love, I am nonetheless looking forward to turning between statisticians and scientists. This conve- it over to a new steward, who would bring new vi- niently coincides with my decision some years ago sion and energy to it. As a second priority for ISBA, to operate primarily as a Bayesian since I believe therefore, I would like to see the establishment of a this is the most natural route to develop and main- transition plan for the journal, with a clear notion tain successful collaborations. More details can be of how editorship will function in steady state. found at http://www.ics.uci.edu/∼wjohnson. ISBA is a strong organization, and it remains for me a primary source of professional identification. Steve MacEachern I trust the bulk of our members feel the same way, and will be willing to work on behalf of furthering Steven MacEachern (Ph.D. 1988, University of Min- ISBA’s goals. nesota) is a Professor in the Department of Statis- tics at the Ohio State University. Steve’s research interests include nonparametric Bayesian methods, Nominees for Board of Directors computational methods, applications of Bayesian 2005–2007 methods to psychometrics, and how to formally in- corporate difficult to quantify information for in- Marilena Barbieri ference. He has published papers in volumes such as the CMU Case Studies in Bayesian Statistics Marilena Barbieri (Ph.D. ’92, Universita` di Roma series and in journals which include Biometrics, “La Sapienza”) is Professor of Statistics, Univer- Biometrika, JASA, JCGS and JRSSB. Steve served sita` Rome Tre, Italy. Her main areas of interest on the ISBA Nominating Committee in 2003. More are Bayesian model selection; time series analysis; information is available at his web site http:// Bayesian computation. She has published papers www.stat.ohio-state.edu/∼snm. on several journals, including Annals of Statistics, Biometrika, IEEE Transactions on Signal Process- Manuel Mendoza ing, Journal of the Italian Statistical Society. She has written an “Introduction to MCMC methods” Manuel Mendoza (PhD 1988, Universidad Na- for the Monograph Series of the Italian Statistical cional Autonoma´ de Mexico)´ is Professor of Statis-

4 tics at the Instituto Tecnologico´ Autonomo´ de research; from my own research I am thinking par- Mexico´ (ITAM) where he also is Director of the Ap- ticularly of machine learning. I believe it is vital plied Statistics Centre and the Risk Management for our profession that we engage with these very master’s program. His research interests include active research communities, to our mutual ad- reference analysis, Bayesian modelling, stochastic vantage. http://www.tcd.ie/Statistics/staff/ processes, time series and applications to finance simonwilson.shtml. and health sciences. He has published in Biomet- rics, Communications in Statistics, Journal of Ap- Brani Vidakovic plied Statistics, Test, Biometrical Journal, Journal of Business and Economic Statistics, North Amer- Brani Vidakovic (PhD Purdue University) is Pro- ican Actuarial Journal and Advances in Economet- fessor of Statistics at Georgia Institute of Technol- rics, among other journals. He has been one of ogy and Adjunct Professor of University of Geor- the organisers of the III World Meeting of ISBA, gia and Emory University. His current research III International Workshop on Objective Bayesian interest include wavelets, in particular Bayesian Methodology and the II Latin American Congress wavelet shrinkage, functional data analysis, mod- on Bayesian Statistics. He was President of the eling of high-frequency data, statistical scaling and Mexican Statistical Association (1998-1999). Bayes-minimax compromise. He has published a book on wavelets and articles in a range of jour- Judith Rousseau nals and edited volumes. He is current president of Georgia ASA section, associate editor of sev- After my Ph.D. in 1997 at the University Paris 6, eral statistical journals, and an editor-in-chief of I have been working until 2004 at the University Wiley’s second edition of Encyclopedia of Statisti- Paris 5 as an Assistant Professor and I am cur- cal Sciences. Brani is a member of ISBA since its rently Professor at the University Paris-Dauphine inception and served on ISBA’s nomination com- (FRANCE) in the department of applied math- mittee (2003-2004) and as a corresponding editor ematics (CEREMADE). My research interests in- of ISBA Journal. (1999-2001). He is also interested clude interactions between Bayesian and frequen- in Bayesian education and created a first course in tist analyses, asymptotics, nonparametric Bayesian Bayesian Statistics at Georgia Institute of Technol- statistics and biomedical applications. I have pub- ogy. http://www.isye.gatech.edu/∼brani. lished papers in Annals of Statistics, Bernoulli, JASA, JCGS, Scandinavian Journal of statistics etc. Jim Zidek Further information about my research can be found in my web-page: http://www.ceremade. Jim Zidek (PhD Stanford, FRSC) I am at the Statis- dauphine.fr/∼rousseau/. tics Dept, U British Columbia. My early interests in the foundations of Bayesian decision analysis Simon Wilson have swung to applications, particularly in environmental science where I have published exten- I am a Senior Lecturer (from Oct 05) in the De- sively, culminating in a co-authored book on mod- partment of Statistics at the University of Dublin, elling environmental space time processes. My ex- Trinity College (Ireland). My areas of interest perience has made me see ISBA as providing a are image processing, distributed computing for unique framework for addressing issues in ”post Bayesian methods, reliability and applications of normal science” (with its radical uncertainty, high Bayesian methods in a variety of other fields. I risks and multiplicity of legitimate perspectives, have published in the Journal of the Royal Sta- eg global climate change). As background, I have tistical Society Series C, Statistics and Computing, served with Morrie DeGroot as an Editor of Statisti- IEEE Transactions on Signal Processing, SIAM Re- cal Science and on Committees as well as Councils view, Advances in Applied Probability and IEEE of the IMS/SSC. I was President of the latter. Hon- Transactions on Reliability. My previous services ors are listed in my full CV reached through http: to ISBA have been to contribute articles to the ISBA //hajek.stat.ubc.ca/∼jim/fullcv.pdf, but in- newsletter. As a board member, I would like to see clude the Gold Medal of the Statistical Soc of ISBA have higher visibility in other fields where Canada as well as Election to the Royal Soc of Bayesian methods are becoming an active topic of Canada. http://www.stat.ubc.ca/people/jim.

5 ISBA Bulletin, 12(3), September 2005 VALENCIA/ISBA INFORMATION

CALLFOR ORAL PRESENTATIONS: as .ps, .pdf or .doc files. ISBA 2006 Abstracts will be accepted between 1st Septem- ber and 30th October 2005. No late submissions by Kerrie Mengersen and Peter Müller will be accepted. The ISBA Conference Programme [email protected] and Committee will review and vote on the submis- [email protected] sions during November and the list of selected pre- The Valencia/ISBA Eighth World Meeting on sentations will be available on the conference web- Bayesian Statistics will be held in Benidorm (Al- site by 15th December 2005. icante, Spain) from June 1st to June 7th, 2006. In keeping with the Valencia/ISBA tradition, this See the conference website http://www.uv.es/ series of oral presentations is intended to comple- ∼bernardo/valenciam.html. ment the conference poster sessions which form the As part of the programme, ISBA is organizing a seminal means of communication of research by limited number of contributed oral presentations. conference participants. A call for posters will be A total of 32 such presentations will be scheduled, made separately. each of 25 minutes duration (20 minutes talk, 5 The ISBA Conference Programme Committee minutes for discussion). comprises the following: Kerrie Mengersen (Aus- If you are interested in giving an oral presenta- tralia, co-chair), Peter Mueller (USA, co-chair), Her- tion at this meeting, you are invited to submit an bie Lee (USA, co-chair Finance), Jose Bernardo abstract of no more than three pages (including ref- (Spain, past Chair; Valencia Programme Commit- erences), accompanied by one additional page list- tee), Subashis Ghosal (USA), Paolo Giudici (Italy), ing no more than five relevant published references Merlise Clyde (USA), Yanan Fan (Australia), Ju- by the author/s. Any additional pages will not be dith Rousseau (France), Cathy Chen (Taiwan), considered. Richard Arnold (New Zealand), Paul Mostert Submissions can be made via email to (South Africa), Robert Wolpert (USA), Josemar Ro- [email protected] Please use the header AB- drigues (Brazil), Jiangsheng Yu (China), Antoni- STRACT NAME where NAME is the first author’s etta Mira (Italy), Mark Steel (UK), Fabrizio Ruggeri name. Attach the abstract and accompanying page (Italy).

ISBA Bulletin, 12(3), September 2005 BAYESIAN HISTORY

THE FERMI’S BAYES THEOREM that of the co-inventor Paul Dirac, and the particles described by the Fermi-Dirac statistics are called by Giulio D’Agostini fermions. [email protected] Among the several other contributions of Enrico Fermi to statistical mechanics, perhaps the most Enrico Fermi is usually associated by the general important is contained in his last paper, written public with the first self-staining nuclear chain re- with John Pasta and Stan Ulam. Without entering action and, somehow, with the Manhattan Project into the physics contents of the paper (it deals with to build the first atomic bomb. But besides these what is presently known as the ‘FPU problem’) achievements, that set a mark in history, his con- it is worth mentioning the innovative technical- tribution to physics - and especially fundamental methodological issue of the work: the time evo- physics - was immense, as testified for example by lution of a statistical system (just a chain of non- the frequency his name, or a derived noun or adjec- linearly coupled masses and springs) was simu- tive, appears in the scientific literature (fermi, fer- lated by computer. The highly unexpected result mium, fermion, F. interaction, F. constant, Thomas- stressed the importance of using numerical simula- F. model, F. gas, F. energy, F. coordinates, F. acceler- tions as a research tool complementary to theoret- ation mechanism, etc.). Indeed he was one of the ical studies or laboratory experiments. Therefore, founding fathers of atomic, nuclear, particle and Fermi, who was unique in mastering at his level solid state physics, with some relevant contribu- both theory and experiments, was also one of the tions even in general relativity and astrophysics. first physicists doing ‘computer experiments’. He certainly mastered probability theory and In fact, with the advent of the first electronic one of his chief interests through his life was the computers, Fermi immediately realized the impor- study of the statistical behavior of physical sys- tance of using them to solve complex problems that tems of free or interacting particles. Indeed, there lead to difficult or intractable systems of integral- is a ‘statistics’ that carries his name, together with

6 differential equations. One use of the computer phans of their untimely dead scientific father, they consisted in discretizing the problem and solv- were in an uneasy position between the words of ing it by numerical steps (as in the FPU prob- the teacher and the dominating statistical culture of lem). The other use consisted in applying sam- those times. Bayes theorem, and especially his ap- pling techniques, of which Fermi is also recognized plication to data analysis, appears in Orear’s book to be a pioneer. It seems in fact, as also acknowl- as one of the Fermi’s working rules, of the kind of edged by Nick Metropolis (http://library.lanl. the ‘Fermi golden rule’ to calculate reaction proba- gov/cgi-bin/getfile?00326866.pdf), that Fermi bilities. Therefore Orear reports of his ingenuous contrived and used the Monte Carlo method to question to know “how and when he learned this” solve practical neutron diffusion problems in the (how to derive maximum likelihood method from early nineteen thirties, i.e. fifteen years before the a more general tool). Orear “expected him to answer method was finally ‘invented’ by Ulam, named by R.A. Fisher or some textbook on mathematical statis- Metropolis, and implemented on the first electronic tics”. “Instead he said, ‘perhaps it was Gauss’ ”. And, computer thanks to the interest and drive of Ulam according to his pupil, Fermi “was embarrassed to ad- and John von Neumann. mit that he had derived it all from his Bayes Theorem”. After this short presentation of the character, This last quote from Orear’s book gives an idea with emphasis on something that might concern of the author’s unease with that mysterious theo- the reader of this bulletin, one might be interested rem and of his reverence for his teacher: “It is my about Fermi and ‘statistics’, meant as a data anal- opinion that Fermi’s statement of Bayesian Theorem is ysis tool. During my studies and later I had never not the same as that of the professional mathematicians found Fermi’s name in the books and lecture notes but that Fermi’s version is nonetheless simple and pow- on statistics I was familiar with. It has then been erful. Just as Fermi would invent much of physics inde- a surprise to read the following recollection of his pendent of others, so would he invent mathematics”. former student Jay Orear, presented during a meet- Unfortunately, Fermi wrote nothing on the sub- ing to celebrate the 2001 centenary of Fermi’s birth: ject. The other indirect source of information “In my thesis I had to find the best 3-parameter fit to we have are the “Notes on statistics for physi- my data and the errors of those parameters in order to cists”, written by Orear in 1958, where the au- get the 3 phase shifts and their errors. Fermi showed thor acknowledges that his “first introduction to me a simple analytic method. At the same time other much of the material here was in a series of discus- physicists were using and publishing other cumbersome sions with Enrico Fermi” and others “in the au- methods. Also Fermi taught me a general method, which tumn 1953” (Fermi died the following year). A he called Bayes Theorem, where one could easily derive revised copy of the notes is available on the the best-fit parameters and their errors as a special case web (http://nedwww.ipac.caltech.edu/level5/ of the maximum-likelihood method” Sept01/Orear/frames.html). Presently this recollection is included in the When I read the titles of the first two sections, freely available Orear’s book “Enrico Fermi, the “Direct probability” and “Inverse probability”, I master scientist” (http://hdl.handle.net/1813/ was hoping to find there a detailed account of the 74). So we can now learn that Fermi was teaching Fermi’s Bayes Theorem. But I was immediately his students a maximum likelihood method “de- disappointed. Section 1 starts saying that “books rived from his Bayes Theorem” and that “the Bayes have been written on the ‘definition’ of probability” Theorem of Fermi” - so Orear calls it - is a special case and the author abstains from providing one, jump- of Bayes Theorem, in which the priors are equally ing to two properties of probability: statistical in- likely (and this assumption is explicitly stated!). Es- dependence (not really explained) and the law of sentially, Fermi was teaching his young collabora- large numbers, put in a way that could be read as tors to use likelihood ratio to quantify how the data Bernoulli theorem as well as the frequentist defini- preferred one hypothesis among several possibili- tion of probability. ties, or to use the normalized likelihood to perform In Section 2, “Inverse probability”, there is no parametric inference (including the assumption of mention to Bayes theorem, or to the Fermi’s Bayes Gaussian approximation of the final pdf, that sim- Theorem. Here we clearly see the experienced plifies the calculations). physicist tottering between the physics intuition, Fermi was, among other things, an extraordinary quite ‘Bayesian’, and the academic education on teacher, a gift witnessed by his absolute record in statistics, strictly frequentist (I have written years number of pupils winning the Nobel prize - up ago about this conflict and its harmful conse- to about a dozen, depending on how one counts quences, see http://xxx.lanl.gov/abs/physics/ them. But in the case of probability based data 9811046). Therefore Orear explains “what the physi- analysis, it seems his pupils didn’t get fully the cist usually means” by a result reported in the form spirit of the reasoning and, when they remained or- ‘best value ± error’: the physicist “means the ‘prob-

7 ability’ of finding” “the true physical value of the pa- ally do: we start from likelihood and prior (often rameter under question” in the interval ‘[best value - uniform or quite ‘vaque’) to get the posterior. In- error, best value + error]’ is such and such percent. stead, Gauss got a general form of likelihood (his But then, the author immediately adds that “the famous error distribution) from some assumptions: use of the word ‘probability’ in the previous sentence uniform prior; same error function for all measure- would shock the mathematician”, because “he would ments; some analytic property of the searched-for say that the probability” the quantity is in that inter- function; posterior maximized at the arithmetic av- val “is either 0 or 1”. The section ends with a final erage of data points. acknowledgments of the conceptual difficulty and Then, why did Fermi mention Gauss for the a statement of pragmatism: “the kind of probability name of the theorem and for the derivation of the the physicist is talking about here we shall call inverse maximum likelihood method from the theorem? probability, in contrast to the direct probability used by Perhaps he had in mind another work of Gauss. the mathematicians. Most physicists use the same word, Or it could be – I tend to believe more this second probability, for the two different concepts: direct prob- hypothesis – a typical Fermi unreliability in pro- ability and inverse probability. In the remainder of this viding references, like in the following episode re- report we will conform to the sloppy physics-usage of the ported by Lincoln Wolfenstein in his contribution word ‘probability’ ”. to Orear’s book: “I remember the quantum mechanics Then, in the following sections he essentially course, where students would always ask, ‘Well, could presents a kind of hidden Bayesian approach to you tell us where we could find that in a book?’ And model comparison (only simple models) and para- Fermi said, grinning, ‘It’s in any quantum mechanics metric inference under the hypothesis of uniform book!’ He didn’t know any. They would say, ‘well, name prior, under which his guiding Fermi’s Bayes The- one!’ ‘Rojanski’, he said, ‘it’s in Rojanski’. Well, it orem held. wasn’t in Rojanski – it wasn’t in any quantum mechan- Historians and sociologists of science might be ics book.” interested in understanding the impact Orear’s I guess that, also in this case, most likely it wasn’t notes have had in books for physicists written in in Gauss, though some seeds were in Gauss. In the the last forty-fifty years, and wonder how they pages that immediately follow his derivation of the would have been if the word ’Bayes’ had been ex- normal distribution, Gauss shows that, using his er- plicitly written in the notes. ror function, with the same function for all mea- Another question, which might be common to surements, the posterior is maximized when the many readers at this point, is why Fermi associ- sum of the squares of residual is minimized. He re- ated Gauss’ name to Bayes theorem. I am not fa- covered then the already known least square prin- miliar with all the original work of Gauss and a ciple, that he claims to be his principle (“principium professional historian would be more appropriate. nostrum”, in Latin) used since 1795, although he ac- Anyway, I try to help with the little I know. In the knowledges Legendre to have published a similar derivation of the normal distribution (pp. 205-212 principle in 1806. Therefore, since Gauss used a flat of his 1809 “Theoria motus corporum coelestium prior, his ‘Bayesian’ derivation of the least square in sectionibus conicis solem ambientum” – I gave a method is just a particular case of the maximum short account of these pages in a book), Gauss de- likelihood method. Fermi must have had this in velops a reasoning to invert the probability which mind, together with Bayes’ name from modern lit- is exactly Bayes theorem for hypotheses that are a erature and with many logical consequences that priori equally likely1 (the concepts of prior and pos- were not really in Gauss, when he replied young terior are well stated by Gauss), and, later, he ex- Orear. tends the reasoning to the case of continuous variables. That is essentially what Fermi taught his [ Some interesting links concerning this subject, collaborators. But Gauss never mentions Bayes, including pages 205-224 of Gauss’ ‘Theoria mo- at least in the cited pages, and the use of the tus corporum coelestium’, can be found in http: ‘Bayesian’ reasoning is different from what we usu- //www.roma1.infn.it/∼dagos/history/.]

1Something similar, also independently from Bayes, was done by Laplace in 1774 (see Stephen Stigler’s ‘The History of Statistics’). However Gauss does not mention Laplace for this result in his 1809 book (while, instead, he acknowledges him for the integral to normalize the Gaussian!). Therefore the ‘Fermi’s Bayes Theorem’ should be, more properly, a kind of ‘Laplace-Gauss Theorem’.

8 ISBA Bulletin, 12(3), September 2005 ANNOTATED BIBLIOGRAPHY

A“BAYESIAN CLASSICS” foundations of statistics which he prepared in con- READING LIST nection with a course at Yale, I have provided an- by Stephen E. Fienberg notations on each of these sources, explaining why [email protected] I think you should want to read each entry. In several instances my short lists overlap with Sav- age’s longer and broader list, and for these papers Introduction and books I’ve reproduced Savage’s annotations following mine in italics. While Bayes’ theorem has a 250-year history and My choices begin with Bayes [16] and Laplace the method of inverse probability that flowed from [21] and then span the 200 plus years that followed, it dominated statistical thinking into the twentieth with a special emphasis on the neo-Bayesian re- century, the adjective “Bayesian” was not part of vival of the 1950s and some of the papers it the statistical lexicon until relatively recently. In my spawned in the following decade. At least three paper for Bayesian Analysis, “When Did Bayesian papers are decidedly not Bayesian, those by Fisher Inference Become “Bayesian”?” [1], I included ref- [20], Neyman [24] and Tukey [29], and another is erences to approximately 170 papers and books. As only incidentally Bayesian, that by Birnbaum [17], work on the paper progressed, I realized how few although several of its discussants including Sav- of the older papers and books were part of mod- age carried the Bayesian message. Two papers are ern statistical education. I also realized the extent from the 1970s. I chose Lindley and Smith [23] be- to which my bibliography would be of only limited cause it represents for many the start of the mod- help to someone approaching this literature for the ern hierarchical Bayesian literature (even though first time. As Jimmie Savage [2] noted: it was preceded by many equally impressive contributions on the topic, e.g., see the discussion Large, unannotated, unclassified bibli- in Fienberg [1]), and Savage’s 1970 Fisher lecture, ographies alphabetized by author are “On Rereading R.A. Fisher,” which was published likely to be a by-product of scholarship. posthumously in 1976. For example, a Xerox copy of such a list My original goal was to have “the top 10 clas- compiled by me is on our shelf. This list sics” for each of books and papers, but limiting the is useful to me because I remember a lit- choice to only 10 proved too difficult a task, and tle something about almost every item presenting a rank-ordering list, in the spirit of those on it and am familiar with the names of on David Letterman’s late-night television show, most of the authors. To sit down and made no sense whatsoever. So, in the end I share pore over such a list will do you little with you my choice of 15 “classic” books (counting good and probably bore you to tears, a pair of multiple volume treatises) and 13 “classic” but it may help you occasionally if you papers, with annotations. Other I suspect would are hunting for works by a specific au- make different choices! thor, and there is always the possibility of alighting on an intriguing title. Annotated bibliographies like the one below seem promising to me. That they References are rarely published is perhaps because it is rash to take the responsibility for [1] Fienberg, Stephen E. (2006). “When did a host of one-line book reviews, often Bayesian Inference Become “Bayesian”?” of books that one has not had time to Bayesian Analysis, 1, 1-40. read but only hopes to some day. There [An essay on the evolution of Bayesian think- is such a bibliography in (Savage [15]). ing from 1973 to the present including an ex- Please look through the entries there planation for why the adjective “Bayesian” that are actually annotated. entered the statistical vocabulary so late. Many Bayesians are surprised to learn who It is my strong belief that a well-educated mod- seems to have been the first to use the term.] ern Bayesian should read to be aware of the historical roots of our methods. Thus I have extracted [2] Savage, Leonard J. (1970). “Reading Sug- two short lists from the longer list of references gestions for the Foundations of Statistics.” in [1], ones of papers and the other of books. In American Statistician, 24, 23–27. [Reprinted the spirit of Jimmie Savage’s [2] reading list on the in Savage, Leonard J. (1981). The Writings of

9 Leonard Jimmie Savage: A Memorial Selection. [7] Good, I.J. (1950). Probability and the Weighing American Statistical Association and Insti- of Evidence. Charles Griffin, London. tute of Mathematical Statistics, Washington, [Good, who was a disciple of Alan Tur- DC, 536–546.] ing, presents an early exposition of subjec- [An eclectic bibliography not only with clas- tive Bayesian approaches to inference includ- sic Bayesian papers and books, but also ing Bayes factors. Savage reviewed this book with papers on inference topics that spaned in JASA, 46 (1951), 383–384, and noted that, the spectrum of the inferential waterfront in while the treatment of axioms was quite clas- 1970. following each entry there is a brief and sical, the book provided a thorough explo- sometimes remarkably frank annotation. For ration of the general principles and included items in the lists below these annotations are “illuminating topics and examples.”] included , in italics.] [8] Good, I.J. (1965). The Estimation of Probabili- Classic Bayesian Books ties. The M.I.T. Press, Cambridge, MA. [The first historical description of the hierar- [3] Blackwell, David and Girshick, Meyer A. chical Bayesian approach to statistical mod- (1954). Theory of Games and Statistical Deci- eling (before the term “hierarchical model” sions. Wiley, New York. (Paperback edition, was coined) with applications to contingency Dover, New York, 1979.) table problems. A slim volume chockful of [A frequentist “bible” for statistical decision interesting ideas.] theory, it also includes some fundamental re- [Savage: A recent and typical work of an ex- sults on the sufficiency of experiments that tremely energetic and original author. Founda- have come to play a mayor role in Bayesian tions and applications are here well mixed.] theory. Blackwell later became a major pro- ponent of the subjective Bayesian approach [9] Jeffreys, Harold (1939). Theory of Probability. to statistics.] Oxford University Press, London. (Third Edi- tion, 1961; also available in paperback, 1998.) [4] Box, George E. P. and Tiao, George C. [This book presents Jeffreys’ integrated “ob- (1973). Bayesian Inference in Statistical Analy- jective Bayesian” perspective. It had a major sis. Addison-Wesley, Reading, MA. influence on the work of leaders of the neo- [One of the first Bayesian texts by key con- Bayesian revival and especially those who tributors in the 1960s. It includes many in- sought an alternative to Savage’s deeply per- sights and techniques that have withstood sonalistic approach to probability and statis- the test of time.] tics. Savage in the paperback edition of [15] [5] de Finetti, Bruno (1974). Theory of Probability. notes that Jeffreys’ book is an “ingenious and Volume I. (1975). Theory of Probability. Volume vigorous defense of a necessary view, similar II. Translated by A. Machi and A. Smith, Wi- to, but more sophisticated than, Laplace’s.” ley, New York. No brief annotation can do it justice. ] [Forty years after his seminal contributions [Savage: A recent edition of a masterpiece that all of the 1930s, de Finetti published this pair of Bayesians should study, though the author is a volumes updating and integrating his ideas nonpersonalistic Bayesian.] on probability and statistics, exchangeability, [10] Kyburg, H.E. and Smokler, H.E. editors etc. These volumes are tough going but re- (1964). Studies in Subjective Probability. Wiley, warding reading, and they have influenced a New York. (Second revised edition, Krieger, generation of Bayesian researchers.] Garden City, 1980.) [6] DeGroot, Morris A. (1970). Optimal Statistical [Two different but overlapping collections Decisions. McGraw-Hill, New York. of classic papers. The 1st edition has sev- [The first post neo-Bayesian revival effort eral historical articles including Savage [27], to present an integrated Bayesian approach whereas the 2nd edition replaced many of to statistical decision theory beginning with these by a different and more recent paper by subjectivist axioms of probability and car- Savage and papers by I.J. Good and Richard rying up through conjugate theory, limiting Jeffrey. Both editions include Ramsay [26] posterior distributions, and sequential deci- and de Finetti [18].] sion making and the sequential choice of ex- [Savage on the 1st Edition: This is an anthology periments.] that I hope we shall all read together.]

10 [11] Laplace, Pierre-Simon (1825). Essai the neo-Bayesian revival. When I was a stu- Philosphique sur les Probabilités. Fifth Edi- dent and a junior faculty member this was a tion Courcier, Paris. Translated by Andrew I. “bible” for Bayesians.] Dale (1995) as Philosphical Essay on Probabili- [Savage: Two books in one. A small but pro- ties, Springer-Verlag, New York. found textbook on Bayesian statistics and a rather [Laplace is easier to read than Bayes, and this large manual of formulas for Bayesian statistics. volume sets forth an accessible version of his The notation may induce nystagmus and split- views on the nature of probability and the ting headaches, but it is not really difficult to method of inverse probability.] learn to read.] [12] Lindley, Dennis V. (1965). Introduction to Prob- [15] Savage, Leonard J. (1954). The Foundations of ability and Statistics from a Bayesian Viewpoint. Statistics. Wiley, New York. (Second revised Part 1: Probability. Part 2: Inference. Cam- paperback edition, Dover, New York, 1972.) bridge University Press, Cambridge. [This was the book that set off the neo- [This two-volume introductory text on prob- Bayesian revival and led to the coining of the ability and statistics emulates what was then term “Bayesian,” although the word does not the usual topics but using “non-informative” appear in the book. The first half presents priors to produce standard distributional a readable and highly original discussion of and other results but in the form of posterior the axioms of probability and utility devel- inferences.] oped from first principles. The second half [Savage: Represents a certain formulation of of the book tries to address some classi- Bayesian statistics not so thoroughly personalis- cal statistical problems from the perspective tic as that of (Raiffa and Schlaifer [14]).] of this axiomatic foundation, unsuccessfully. Following its publication in 1954, Savage be- [13] Mosteller, Frederick and Wallace, David came a committed subjectivist and helped to L. (1964). Inference and Disputed Author- convert many to the Bayesian camp. The pa- ship: The Federalist. Addison-Wesley, Read- perback edition which remains in print in- ing, MA. (The 2nd Edition appeared as Ap- cludes some updated footnotes and bibli- plied Bayesian and Classical Inference–The Case ographic materials. Every Bayesian should of the Federalist Papers. Springer-Verlag, New own a copy.] York, 1984.) [Savage: Consists in part of an axiomatic study [The first large-scale statistical approach to of personal probability and utility merging ideas text classification including their applica- of de Finetti and of von Neumann and Morgen- tion to the disputed Federalist Papers, au- stern. A not very successful attempt is made to thored by Hamilton and Madison. The au- discuss the minimax principle and other devices thors present a host of hitherto unknown of the Neymann-Pearson school. The treatments tools and techniques (e.g., Laplace’s method) of sufficiency and point estimation are relatively and implement them in one of the first major successful. computer-based statistical application. The 2nd edition includes a much updated bibli- Few of you will want to read this book through, ography. The study and methods weather the but since it represents an important part of my test of time and should be read by anyone an- preparation for the course, you may want to take alyzing text data.] a look at it. The author of this book, though interested in personal probability, was not yet a per- [14] Raiffa, Howard and Schlaifer, Robert (1961). sonalistic Bayesian, and he was unaware of the Applied Statistical Decision Theory. Division likelihood principle. The bibliography is useful, of Research Graduate School of Business and this present bibliography is well regarded as Administration, Harvard University, Boston. an extension of it.] (Paperback edition, MIT Press, Cambridge, 1968). Classic Bayesian Papers [The authors develop a Bayesian theory for exponential families and provide the first [16] Bayes, Thomas (1763). “An Essay Towards integrated theory of conjugate prior distri- Solving a Problem in the Doctrine of butions. They coin the term and provide Chances.” Philosophical Transactions of the a detailed implementation. The entire book Royal Society of London 53, 370–418. [Pub- seems to have been developed totally sep- lished in 1764; reprinted, with an introduc- arately from Savage and others involved in tion in Barnard, George A. (1958). “Stud-

11 ies in the History of Probability and Statis- [20] Fisher, R. A. (1922). “On the Mathematical tics: IX. Thomas Bayes’ Essay Towards Solv- Foundations of Theoretical Statistics.” Philo- ing a Problem in the Doctrine of Chances.” sophical Transactions of the Royal Society of Lon- Biometrika, 45, 293–315.] don, Series A, 222, 309–368. [Bayes’s posthumously publish paper is the [ As Stigler recently noted in Statistical Sci- earliest exposition of Bayes’ theorem and ence 20 (2005), 3249: “Ronald A. Fishers 1921 an interesting application of a priori think- article on mathematical statistics (submitted ing. Some have argued that it owes more to and read in 1921; published in 1922) was Richard Price (who edited it) than to Bayes. arguably the most influential article on that This is not an easy read.] subject in the twentieth century...” The article introduces most of modern statistical [17] Birnbaum, Allan (1962). “On the Founda- concepts such as sufficiency, efficiency, esti- tions of Statistical Inference (with discus- mation, likelihood, and consistency, as well sion).” Journal of the American Statistical Asso- as the word “parameter” and the notion of ciation, 57, No. 298, 269-326. [Discussion by parametric families. In one fell swoop, Fisher L. J. Savage; George Barnard; Jerome Corn- presented a new and almost mature theory field; Irwin Bross; George E. P. Box; I. J. Good; of estimation on which Bayesians and non- D. V. Lindley; C. W. Clunies-Ross; John W. Bayesians have since built. ] Pratt; Howard Levene; Thomas Goldman; A. P. Dempster; Oscar Kempthorne; and a re- [21] Laplace, Pierre-Simon (1774). “Memoire´ sponse by Allan Birnbaum.] sur la Probabilite´ des Causes par les [In his discussion of this paper and in later ev´ enements,”´ Mémoires de mathématique writings, Savage stressed the importance of et de physique presentés á l’Académie royale Birnbaum’s work and the likelihood princi- des sciences, par divers savans, & lûs dans ple for completing the Bayesian framework ses assemblées, 6, 621–656. Reprinted in for inference.] Laplace’sOeuvres complétes, 8, 27–65. (English translation and commentary by Stephen [Savage: An important analysis and defense of M. Stigler in Statistical Science, 1, (1986), the likelihood principle.] 359–378). [18] de Finetti, Bruno (1937). “La prevision:´ ses [Laplace reinvented Bayes’ theorem here, in a lois logiques, ses sources subjectives,” An- more general form than Bayes. His approach nales de l’Institut Henri Poincaré, 7, 1–68. later became known as the method of in- Translated as “Foresight: Its Logical Laws, verse probability. The English translation of Its Subjective Sources,” in H. E. Kyburg, H.E. Laplace’s paper is well worth reading, in part and Smokler, H.E. eds., (1964). Studies in Sub- because of the commentary by Stigler.] jective Probability. Wiley, New York, 91–158. [An overview of subjective probability and [22] Lindley, Dennis V. (1957). “A Statistical Para- exchangeability based on 4 lectures given dox.” Biometrika, 44, 187–192. in Paris, that summarizes de Finetti’s ba- [In this brief paper, Lindley demonstrates the sic ideas on the topic. A difficult read, but possible contradiction between the results of worth the effort. de Finetti stresses differ- a test of significance and an assessment of ent implications of his representation theo- the posterior probability of a null hypothesis. rem that those usually emphasized by mod- He also relates these ideas to the frequentist ern Bayesians.] problem of optimal stopping when the likelihood function does not depend on the stop- [19] Edwards, Ward, Lindeman, H. and Savage, ping rule. Many Bayesian and non-Bayesian Leonard J. (1963). “Bayesian Statistical Infer- observers returned to this paradox in subse- ence for Psychological Research.” Psychologi- quent papers and commentaries.] cal Review, 70, 193–242. [This paper is perhaps the most readable ex- [23] Lindley, Dennis V. and Smith, Adrian F.M. position of the Bayesian position in the early (1972). “Bayes Estimates for the Linear post neo-Bayedsian revival literature, includ- Model (with discussion).” Journal of the Royal ing a discussion of the robustness of poste- Statistical Society, Series B, 34, 1–44. rior inferences to prior specification.] [This classic paper is the one that most mod- [Savage: A fairly complete but relatively amathe- ern Bayesians cite as the origin of hierarchical matical discussion of Bayesian Statistics.] Bayesian modeling, although the discussion

12 makes clear that the ideas had been devel- tion of “value” or utility. Starting from some oped by many others over an extended pe- basic axioms on values, Ramsey derives sev- riod of time. The paper give an integrated eral of the elementary axioms of probability. treated of the hierarchical approach to nor- Savage in the paperback edition of [15] de- mal theory problems. While the paper had scribes it as being a “Penetrating develop- many precursors, especially in the work of ment of a personalistic view of probability I.J. Good, few were able to so elegantly lay and utility.”] out a path for others to follow.] [27] Savage, Leonard J. (1961). “The Foundations [24] Neyman, Jerzy (1934). “On the Two Differ- of Statistical Inference Reconsidered.” Pro- ent Aspects of the Representative Method: ceedings of the Fourth Berkeley Symposium on The Method of Stratified Sampling and the Mathematical Statistics and Probability, Uni- Method of Purposive Selection (with discus- versity of California Press, Berkeley, 1, 575– sion).” Journal of the Royal Statistical Society, 586. [Reprinted in Kyburg, H.E. and Smok- 97 , 558–606. ler, H.E. eds. (1964). Studies in Subjective Prob- [Neyman’s classic paper on sampling de- ability. Wiley, New York, 173–188, and in scribes the methods of stratification, cluster- Savage, Leonard J. (1981). The Writings of ing, and optimal allocation. Bayesians need Leonard Jimmie Savage: A Memorial Selection. to read the arguments carefully to iden- American Statistical Association and Insti- tify Neyman’s repeated sampling perspec- tute of Mathematical Statistics, Washington, tive and to understand the design versus DC, 296–307.] model-based divide that is so prominent in [This paper and a closely related discussion the field of sampling. But as important as paper read to the Royal Statistical Society at the paper was for sampling, it may well be about the same time signaled the maturation even more important because it was here of Savage’s views on the foundations and the that Neyman introduced the concept of con- importance of such key ideas as the role of fidence intervals, a notion referred to in the the likelihood principle.] discussion by Fisher as “a confidence trick.”] [Savage: Presents some criticism of (Savage [25] Pratt, John W. (1965). “Bayesian Interpreta- 1954) and gives a concise account of Bayesian tion of Standard Inference Statements.” Jour- statistics.] nal of the Royal Statistical Society. Series B, 27, [28] Savage, Leonard J. (1976). “On Rereading R. 169–203. A. Fisher (with discussion)(J.W. Pratt, ed.).” [A Bayesian looks ingeniously for points of Annals of Statistics, 4, 441—500). [Reprinted reconciliation between Bayesian theory and in Savage, Leonard J. (1981). The Writings of non-Bayesian procedures. Pratt sums up by Leonard Jimmie Savage: A Memorial Selection. observing that “a Bayesian can make consid- American Statistical Association and Insti- erable use of some standard methods. A non- tute of Mathematical Statistics, Washington, Bayesian, if he feels there is some element of DC, 678–720.] sense in some Bayesian point of view in some [This was Savage’s 1970 Fisher Lecture at circumstances, may expect a Bayesian lamp the American Statistical Association Annual to throw some light on his methods.”] Meeting at which he held an overflowing [26] Ramsey, Frank Plumpton (1926). “Truth and room spellbound for almost two hours. Lov- Probability” written 1926. Published in 1931 ingly edited by John Pratt with discussion as Foundations of Mathematics and Other Log- by Churchill Eisenhart, D.A.S. Fraser, V.P. ical Essays, Ch. VII, pp. 156–198. Edited Godambe, I.J. Good, Oscar Kempthorne, by R.B. Braithwaite. Kegan, Paul, Trench, and Stephen Stigler, and most especially Trubner & Co., London. (Reprinted in Ky- Bruno de Finetti. Savage examines Fisher’s burg, H.E. and Smokler, H.E. eds. (1964). great ideas here lovingly, but not uncriti- Studies in Subjective Probability. Wiley, New cally. Pratt’s abstract summarizes Savage’s York, 61–92.) [Electronic edition available perspective: “Fisher is at once very near to at: homepage.newschool.edu/het/texts/ and very far from modern statistical thought ramsey/ramsess.pdf] generally.”] [This is a relatively brief paper that argues [29] Tukey, John W. (1962). “The future of data for the subjective approach to probability, la- analysis.” Annals of Mathematical Statistics, 33, belled as degree of belief, from a simple no- 1–67. (corrections, p. 812.)

13 [An areligious paper that is not speciﬁcally on ways this is one of Tukey’s more accessible foundations but one which signaled a new papers.] focus on data analysis instead of mathematical statistics, and spawned many implemen- [Savage: Words fail me. Difﬁcult, important, tations in the decades to follow. In many slippery. We should all tackle it together.]

THE 2006 MITCHELL PRIZE The Mitchell Prize committee invites nominations for the 2006 Mitchell Prize. The Prize is currently awarded every other year in recognition of an out- standing paper that describes how a Bayesian analysis has solved an important applied problem. The Prize is jointly sponsored by the ASA Section on Bayesian Statistical Science (SBSS), the International Society for Bayesian Analysis (ISBA), and the Mitchell Prize Founders’ Committee, and consists for 2006 of an award of $1000 and a commemorative plaque. The 2006 Prize selection committee members are Tony O’Hagan (chair), Dave Higdon and Marina Vannucci. This information is reproduced from http://www.bayesian.org/ awards/mitchell.html, where more details may be found.

ISBA Bulletin, 12(3), September 2005 STUDENT CORNER

A primary feature of the Student Corner section available, in the literature, but the possibilities for is the publication of dissertation abstracts. If you multivariate constrained testing are limited. A have recently defended your Ph.D. thesis, please computational method to sample the null distri- email the abstract to [email protected]. bution of any test statistic in the context of both For the september issue we have one abstract. univariate and multivariate constrained alternative hypotheses is presented. The brunt of the thesis discusses Bayesian esti- INEQUALITY CONSTRAINED mation and model selection in the context of (com- NORMAL LINEAR MODELS peting) inequality constrained normal linear models. It is natural to encode the inequality constraints by Irene Klukist in the prior distribution of the model parameters. [email protected] Each theory constitutes its own prior knowledge http://www.fss.uu.nl/ms/ik and therefore the appropriate prior is defined for Faculty of Social Sciences, Utrecht University each model. A motivation for Bayesian model se- Supervisor: Prof. dr. Herbert Hoijtink lection is provided in preference to null hypothesis testing. Dissertation Abstract Next, the idea of encompassing priors is intro- This dissertation deals with normal linear mod- duced and examined. Since inequality constrained els with inequality constraints among model pa- models are all nested in one unconstrained, encom- rameters. Scientists often have one or more the- passing model, just one prior needs to be specified. ories or expectations with respect to the outcome The prior distributions for the constrained models of their empirical research. To evaluate these theo- are derived by a truncation of the parameter space. ries they have to be translated into statistical mod- Sensitivity analysis can provide information about els. When scientists talk about the expected rela- the fit of each of the models, that is, of each of the tions between variables if a certain theory is cor- theories. Sensitivity analysis of encompassing pri- rect, their statements are often in terms of one or ors can also show that for specific classes of models more parameters expected to be larger or smaller the selection is virtually objective, that is, indepen- than some of the others. In other words, their dent of the encompassing prior. The encompassing statements are often formulated using inequality prior also leads to a nice interpretation of Bayes fac- constraints. Frequentist null hypothesis testing tors. The Bayes factor for any constrained model with inequality constrained alternatives are inves- with the encompassing model reduces to the ratio tigated. Test for univariate normal models are of two proportions, namely the proportion of the

14 encompassing prior and posterior, in agreement Bayes factors for all pairs of models are obtained. with the constraints. This enables efﬁcient estima- The thesis closes by illustrating the potential of tion of the Bayes factor and its standard error since posterior model probabilities and model selection with only one sample from the encompassing prior as an alternative to the use of p-values in traditional and one sample from the encompassing posterior, hypothesis testing.

ISBA Bulletin, 12(3), September 2005 NEWS FROM THE WORLD

NEWSFROMTHE WORLD • Jose´ Galvao˜ Leite (UFSCar) by Alexandra M. Schmidt • Helio Migon (UFRJ) [email protected] • Ajax Moreira (IPEA) I would like to encourage those who are organi- • Marina Paez (UFRJ) zing any event around the World, to get in touch • with me to announce it here. Fabrizio Ruggeri (CNR-IMATI, Italy) • Nicholas Polson (University of Chicago) Events • Alexandra M. Schmidt (UFRJ) • Mark Steel (University of Warwick) Evidence Synthesis for Decision Modelling, Bur- walls, Bristol, UK. December 5th - 9th, 2005. • Mike West, (Duke University) This course is a 5-day course intended for: (a) Anyone undertaking health technology assess- The Chair of the conference is Professor Marco A. ments, including cost-effectiveness analyses, (b) R. Ferreira ([email protected]). Information about Statisticians, with or without experience in meta- the program, travel, accommodations, and regis- analysis, who wish to learn about Bayesian meth- tration will be available on the conference website ods for evidence synthesis particularly in the con- shortly. text of cost-effectiveness analysis. The Meeting will feature invited talks, con- Course Organizers: Prof Keith Abrams (Univ of tributed talks and posters. If you would like to con- Leicester), Prof Tony Ades (MRC HSRC, Bristol), tributed with a talk or poster, please submit a title Dr Nicola Cooper (Univ of Leicester), Dr Alex Sut- and abstract to [email protected]. ton (Univ of Leicester) and Dr Nicky Welton (MRC For more information, please contact one HSRC, Bristol) of the members of the Scientiﬁc Committee: Further details including online booking can be Marco A. R. Ferreira ([email protected]), Dani found at the course website http://www.hsrc.ac. Gamerman ([email protected]), Hedibert F. Lopes uk/EvidenceSynthesis2005/evsynth main.htm ([email protected]), Rosangela H. Loschi and from the Course Administrator Sarah Garbutt ([email protected]), Josemar Rodrigues (vjose- (Email [email protected] or Tel +44 [email protected]). (0)117 928 7262). International Conference on Inverse Problems: Eighth Brazilian Meeting on Bayesian Statis- Modeling and Simulation Fethiye, Turkey. May tics in Honor of Helio Migon. March 26-29, 2006. 29-June 2, 2006. Colonna Park Hotel, Buzios, Rio de Janeiro, Brazil. This conference might be of interest to the The meeting celebrates the 60th anniversary of Bayesian Statistical Community in Inverse or Ill- Professor Helio S. Migon. Helio has been one of Posed Bayesian Problems. the main forces behind the Bayesian Brazilian surge The main aim of the Conference is to combine over the last 15 years and, in particular, one of presentations in the theory and applications of in- the leaders of the Graduate Program in Statistics at verse problems from groups all over the world. It Universidade Federal do Rio de Janeiro where he will bring together all classical and new inverse advised some 30 master and Ph.D. students. problems from international scientiﬁc schools. The The invited speakers for the conference are: focus will be on new challenges of inverse problems in current interdisciplinary science and future • Marcia´ Branco (USP) directions. The proposed International Conference will be under the auspices of the leading inter- • Ricardo Ehlers (UFPR) national journals Inverse Problems, Inverse Prob- • Edward George (University of Pennsylvania) lems in Science and Engineering and Inverse and Ill-Posed Problems. More details can be found at • Pilar Iglesias (PUC, Chile) http://umm.kou.edu.tr/kongre/.

15 Executive Committee Program Council Board Members

President: Sylvia Richardson Chair: Kerrie Mengersen Carmen Fernandez, Valen Johnson, Past President: Jim Berger Vice Chair: Peter Muller¨ Peter Muller,¨ Fernando Quintana, President Elect: Alan Gelfand Past Chair: Jose´ Miguel Bernardo Brad Carlin, Merlise Clyde, David Treasurer: Bruno Sanso´ Higdon, David Madigan, Michael Executive Secretary: Web page: Goldstein, Jun Liu, Christian Robert, Deborah Ashby http://www.bayesian.org ¨ Marina Vannucci. EDITORIAL BOARD©

Editor

J. Andres´ Christen

Associate Editors

Annotated Bibliography Alexandra M. Schmidt Marina Vannucci Software Review Applications Ramses Mena Catherine Calder Student’s Corner Interviews Robert Gramacy Bayesian Brunero Liseo History News from the World Antonio Pievatolo