December 2012 the Oﬃcial Bulletin of the International Society for Bayesian Analysis

THE ISBABULLETIN

Vol. 19 No. 4 December 2012 The oﬃcial bulletin of the International Society for Bayesian Analysis

A MESSAGE FROM THE PRESIDENT

- Fabrizio Ruggeri - wish them a successful result. I hope my friends ISBA President, 2012 in Latin America will follow my suggestion (but [email protected] keeping the longstanding, successful events like EBEB!): there are great opportunities for Baye- This is my last column as ISBA President and sians in your part of the world and, last but not I would like to summarise the achievements of least, attending a meeting in Latin America is a very exciting year, which reached its apex in always an unforgettable experience for people Kyoto where we had the largest World Meeting coming from the rest of the world. in ISBA history (and the next one in Cancun, Mexico, in 2014 might be even larger: so mark This year we approved, after 20 years of provi- your calendar for mid July 2014!). I would like sional policy, bylaws on how chapters are formed to thank one more time Igor Pruenster, Hajime and operated, and interact with ISBA. Precise ru- Wago and Yasuhiro Omori for the great scientific les should make the creation of new chapters ea- programme and organisation of ISBA 2012. sier: we just need volunteers (like in Mexico) willing to undertake the goal! In my statement for the 2010 elections I had ... Continued on page 2. identified three major areas for ISBA expansion: countries outside our strongholds (USA and Europe), scientists in other fields and young sta- In this issue tisticians. I am glad to report that the first Latin American summer school in Bayesian Statistics ➤ FROM THE PROGRAM COUNCIL (with Raquel Prado and Luis Raul Pericchi as lec- ☛Page 6 turers) will be held in Costa Rica in July 2013, fol- ➤ FROM THE BOARD OF DIRECTORS lowed by a meeting (see my short note elsewhere ☛Page 7 in the Bulletin). This year the official language of both events will be Spanish to promote diffusion ➤ 2012 ISBA ELECTION ☛Page 8 of Bayesian ideas without language barriers. IS- BA will provide its “usual” support to students ➤ SUMMER SCHOOL and young researchers. The next schools will be ☛Page 9 in Mexico near Cancun in 2014 before the IS- ➤ A MESSAGE FROM THE BA EDITOR BA World Meeting and in Medellin (Colombia) ☛Page 10 in 2015 before COBAL 4. I think both COBAL ➤ ISBA - SECTIONS and the summer school should be organised on ☛Page 10 a regular basis by the Latin American chapters, involving also Bayesians in countries without a ➤ SOFTWARE HIGHLIGHT ☛Page 14 chapter. A contribution in such direction could be provided also by the possible creation of a new ➤ NEWS FROM THE WORLD Mexican chapter which is currently pursued by ☛Page 20 Manuel Mendoza and Eduardo Gutierrez-Pe´ na:˜ I ISBA Bulletin, 19(4), December 2012 A MESSAGE FROM THE PRESIDENT

MESSAGE FROM THE PRESIDENT, Conti- chaired this year by Kate Calder. If you missed nued from page 1. ... the very successful first one by Mark Berliner, you can see the video on the web (where you I hope new chapters will start in other parts will find also the videos of the four “ISBA Lectu- of the world: Japan and China could be possi- res on Bayesian Foundations” given in Kyoto by ble “targets” for the future, building on the very Don Berry, Christian Robert, Aad van der Vaart successful ISBA World Meeting in Kyoto and the and Mike West). I would like to thank the Pro- many possibilities offered nowadays in China gramme Committee, chaired by Vanja Dukic, for (where the Objective Bayes section is going to ha- the excellent work done not only for Kyoto but ve a regional meeting, after a worldwide one last also for all the other events realised this year or year, organised by Dongchu Sun). Colleagues in planned for the future. Australia are continuing their very intensive activities (especially enjoying “Bayes on the Beach”), The second point in my 2010 statement was whereas Satyanshu Upadhyay has organised in about interaction with scientists in different January 2013 a “regional” meeting in Varanasi fields. This year we have created many new sec- (India), which is actually a sort of world mee- tions which should help in achieving such goal ting, given the number of participants and their (and the success depends on you and your con- affiliations. In Vietnam, ISBA is endorsing a contribution!). We have now sections on Economics, ference next June and organising a course (given Finance and Business, on Industrial Statistics, by Christian Robert), whereas I am working for on Biostatistics and Pharmaceutical Statistics, on a Bayesian meeting in Saudi Arabia in January Environmental Sciences (to be approved before 2014. I tried to promote a North African mee- the end of the year). A section on Astrophysics ting in Algeria but it did not work out because of (or Physical Sciences) was discussed and there lack of funds (but I am not giving up since the- was a decision to postpone its creation since so- re is interest for Bayesian methods over there). me of the possible leaders are currently involved A different (positive!) result has been obtained in the creation of a more general society in the by Lizanne Raubenheimer who is organising a field. I hope those sections will be able to interact South African chapter meeting next June. As you with scientists and practitioners, through com- can see, some work has been done to promote mon work, projects, meetings, courses, books, Bayesian ideas in countries around the world but and teaching. As an example, I just proposed the a lot more can be done! Industrial Statistics Section Chair, Refik Soyer, to prepare an edited book on (advanced) case stu- On a personal side, I hope I will have the op- dies in Bayesian Industrial Statistics: such a book portunity to contribute to the diffusion of sound does not exist and it could give visibility to the statistical methods in those countries in my new section, besides some revenues: it is a sort of co- position (as of September 2013) as member of the meback, on a smaller scale, of my earlier idea of Council of the International Statistical Institute (a a series of ISBA books which was not approved nomination and an election which were definite- by the ISBA Board after a debate on feasibility, ly affected by my role in ISBA, and not only in IS- product quality and benefits, like those offered BIS, an ISI association on business and industrial by two publishers interested in the idea. statistics). We have not forgotten USA/Canada and Europe: ISBA will be a Joint Statistical Mee- This year we built a structure, identifying to- tings partner from 2013 (thanks to the work of the pics for possible sections, inviting people to crea- Past President Michael Jordan) whereas Christi- te new ones and accepting proposals, and crea- an Robert will give a distinguished lecture on the ting bylaws which should clearly define interac- 250th anniversary of Bayes Theorem at the 29th tions between ISBA and its sections and section European Meeting of Statisticians in Budapest. organisation. Now the tough job is ahead: the There is also a long list of meetings organised structure has to be filled with valuable content! by our sections or endorsed by ISBA: follow the The sections should make a difference in the co- ISBA Forum or browse through the ISBA website operation with people in other fields and both and you will (almost) surely find events of your spread the use of sound Bayesian methods and interest which are, probably, near you. If not, then get new lymph from the interaction. Traditional wait for the next webinar, organised by the new- methods, like the ones I just mentioned, should ly appointed Continuing Education Committee, be pursed but they might not be sufficient: sec-

Content 2 www.bayesian.org ISBA Bulletin, 19(4), December 2012 A MESSAGE FROM THE PRESIDENT tion officers and members have to find effective one of the four officers!). I hope also that young ways to interact and communicate with scientists Bayesians will be involved as Editors of the ISBA and practitioners. I recently asked Dalene Stangl Bulletin: their enthusiasm could be very helpful and Jim Albert of thinking about the feasibility of for its continuing success. Another contribution, a section on Teaching Bayes, to promote diffusion for sure important for ISBA (but probably also of Bayesian courses, mostly in universities. ISBA for young people), could come from maintaining could develop material (books, software, video some parts the ISBA website and helping for the lectures, and slides) which could be accessed by technical aspects of the webinars. Since we are people willing to promote the study of Bayesi- expanding the content of our website and star- an statistics in universities where “Frequentist ting a series of webinars, ISBA webmaster and Statistics” is often synonym of “Statistics”. We Continuing Education Committee might need could target some geographical areas (e.g. Latin some help (and bylaws allow!) and young peo- America and China) and fields of study, like Bio- ple are more accustomed than older people like logy and Engineering, preparing ad hoc material me for this kind of job. Finally, the creation of (e.g. in Spanish or Chinese or with biological or new sections could provide many young people engineering examples). A relevant role in promo- the opportunity to take responsibilities within IS- ting Bayesian methods can be played by another BA: I hope current section officers will share my new section, the one on Bayesian computation. opinion and act accordingly. My advice to its section officers, especially after a chat with a senior (frequentist) statistician During the year we had many contacts with about Bayes and industrial statistics, is that the other societies, first of all SBSS, the Bayesian sec- section should be not only a community within tion of ASA, trying to deepen the current coope- the Bayesian world, developing more and more ration about awards. We had also contacts with sophisticated and/or efficient methods and pre- ASA, IMS, Bernoulli, ISI, SIS (Italian Statistical senting them in cool meetings like MCMCSki, Society), just to mention few. I am glad to report but also a promoter of (free and/or commercial) that, thanks to the work of the people who came software which people in companies/industries before us, ISBA has an important, very well re- could easily use to perform Bayesian analyses. cognised role in the statistical community world- We should think of the many people outside of wide. academia who would like just to push a button and get reliable results which solve their pro- We worked a lot also to “clean the house”, blems. approving many bylaws which should make IS- BA more efficient, setting well defined policies, Last, but not least, I thought that young Baye- and we improved the Book of Procedures star- sians should be more and more involved in IS- ted last year which should help in keeping track BA activities. This year j-ISBA has been created, of who is going to do what, when and how, wi- a successful kickoff meeting was held in Kyo- thout being subject to “wheel reinvention” after to (with some extra social events), a meeting is each change in ISBA officers. Here I would like planned next June in my institute in cooperati- to thank the Constitution and Bylaws Commit- on with the young members of the Italian Sta- tee, chaired by David Madigan, which went very tistical Society (and I hope there will be others carefully through the many bylaws we approved in the following years in different parts of the and gave suggestions on how to improve them world), an invited section will be organised in and make them consistent with the Constitution a meeting in Ireland endorsed by the Industrial and the existing bylaws. Statistics Section in July, something will happen at the Bayesian Nonparametrics meeting in Am- We have completed the transition from the sterdam in June and many other events are in “old” bayes-news and Valencia meeting mailing the minds of Andrew Cron, Marian Farah, Fran- lists to the Bayes Forum. Now ISBA is providing cesca Ieva and Perla Reyes. I invite organisers of the most important service to get and submit in- ISBA events to get in touch with j-ISBA officers formation of interest for Bayesians. Our website to promote young people participation: there are is providing a lot of information as well and a many possibilities, from invited sections to tu- lot of work, probably unnoticed by you, has been torials, prizes and social events (and even more: done to efficiently improve handling of many ad- my imagination is limited with respect to the ministrative tasks, communication within ISBA

Content 3 www.bayesian.org ISBA Bulletin, 19(4), December 2012 A MESSAGE FROM THE PRESIDENT committees and to/from members. It has been to honour the winners of this year’s awards. We an impressive work and we should thank Merli- have been working, since last year, to increase se Clyde, Chris Hans and Lance Brown. I am just the funds in the endowments of each award to giving you a warning: as soon as Merlise will guarantee self-sustainability despite the turmoil become President you should learn what Drupal in financial markets. We considered various op- and CiviCRM are (like I did!). tions, including the possibility of reducing the amount of the cash award or eliminating the one We appointed, based on the nominations by for Honourable Mentions in the Savage Award, the Editor Search Committee chaired by Alicia but then we undertook a campaign targeted to Carriquiry, three new ISBA Editors: Marina Van- ISBA members, especially past recipients of the nucci, Feng Liang and Jarad Niemi will replace awards, which provided us enough resources to Herbie Lee, Manuel Mendoza and Chris Hans as be safe in the next few years. I acknowledge the Editors of Bayesian Analysis, ISBA Bulletin and generous support by those members and I invite ISBA website, respectively. The three outgoing all of you to support the awards through dona- editors did a great job and we expect the same tions to their funds, without forgetting the Pilar from the new ones! Bayesian Analysis has be- Iglesias Fund to support participation of young en moved to the IMS system and Project Euclid: statisticians from developing countries to ISBA now handling of submissions will be easier and World Meetings. visibility of the journal will increase a lot (and, hopefully, the impact factor as well, although it After the long list of successes, it is time to is already quite high). I would like to thank the mention where some troubles are: finance! IS- Department of Statistics at Carnegie Mellon, and BA has a lot of reserves in its bank account but especially Rob Kass, for providing a very valua- we have also a lot of expenses. The expansion of ble support in setting up and operating the old ISBA requires clerical work and help with the Bayesian Analysis system. website: the Department of Statistical Science at Duke University, chaired by Alan Gelfand The Nominations Committee, chaired by Mi- (whom I thank), is providing us a lot of help ke Jordan, selected an excellent set of candidates but we have to pay a friendly, but significant for and choosing among them was very difficult (as our finances, amount for such work. The move an example, I think both my friends Sonia Pe- of Bayesian Analysis to the new system had in- trone and Eduardo Gutierrez´ Pena˜ deserved to itial setup costs and there are also annual ones. become President. I hope Eduardo will have ano- More than 150 students and young researchers ther chance!). I would like to thank all those who were supported (mostly by ISBA) to attend the accepted to run: the “winners” have a tough job Kyoto meeting: this is one of our major goals but ahead whereas I hope the “losers” will have other it has a cost! We also supported young people opportunities (I lost three times: twice when run- at other conferences. For all such expenditures ning for President and once in 1994 when I was there should be an equivalent income to ensure nominated for Secretary). This year we decided long term financial safety. We decided to appoint (and modified the bylaws) that, from now on, a Finance Committee, chaired by the Past Presi- sections should choose the nominees for their dent (Mike Jordan, for few weeks more, and then elections, instead of having them selected by the it will be my turn), who should advise the Exec ISBA Nominations Committee. The decision gi- and the Board on investment policies. We have ves more responsibility to the sections, allows for decided to raise the membership fees, still lower selection by people who know better those who than many other statistical societies, but you can could deserve to be the next officers and relieves pay the 2012 rate if you renew your membership the ISBA Nominations Committee from a com- by December, 31st. plex task, sometimes made even harder by the lack of members of the interested sections in it. We are now going to vote the introduction of Institutional Membership, especially for univer- Another outstanding job has been done by the sity departments, publishers and software devel- Prize Committee, chaired by Mark Steel, in char- opers: we will provide them some benefits (free ge of DeGroot Prize, Lindley Prize, Mitchell Prize memberships for some associates, discounts on and Savage Award. We had ceremonies in Kyoto ISBA events, and some ads in the website and and at the SBSS mixer at the JSM in San Diego in the Bulletin) but we should get a significant

Content 4 www.bayesian.org ISBA Bulletin, 19(4), December 2012 A MESSAGE FROM THE PRESIDENT income out of it. We are investing in courses, Researchers Travel Award, Pilar Iglesias Travel especially in webinars, to increase incomes and Award, ISBA Lifetime Members Junior Resear- we have created a Continuing Education Com- chers Award) with a major change: the Lifeti- mittee which is in charge of them. The meeting in me Members award will be more prestigious to Kyoto has been excellent and the organisers wor- recognise junior researchers, attending a World ked hard to reduce the expenses, but the cost of Meeting, who will have given significant contri- life in Japan was so high that no revenue came to butions in the early stage of their career. ISBA out of the World Meeting. I am sure Andres Christen, the organiser of ISBA 2014, is operating Certificates of Appreciation were already pre- in a better situation from the point of view of sent in our bylaws but they were given only twice costs and we also expect an even larger number in ISBA history. Now they should be given more of participants, given that Cancun is a very popu- regularly, but sparingly not to diminish their va- lar place, served by many airlines, with relatively lue, to recognise an outstanding service to ISBA. cheap tickets. From ISBA 2014 we should expect We are going to replace the Founders Award with a significant income to ISBA to relief our finan- another award named after the only person who cial situation (for the moment we have paid the got it and was the leading force in founding IS- Cancun Convention Centre a consistent amount BA: the Zellner Medal. The medal, given at each ...). World Meeting at two (at most) persons, will recognise ISBA members who will have rendered The major income for ISBA comes from the exceptional and distinguished service to ISBA membership fees and I warmly invite you to re- over an extended period of time. Finally, we are new your membership, possibly adding some going to introduce ISBA Fellows, elected at each sections of your interest and donating to our World meeting and recognising ISBA members funds. Only in this way it will be possible for who will have made outstanding contributions ISBA to guarantee services like Bayes Forum, in some aspect of statistical work (publication, te- website, meetings, courses, video lectures, Baye- aching, service, etc.). We have already identified sian Analysis, Bulletin, prizes, travel awards, etc. the first set of fellows but you will know their I am very glad to report that today ISBA has names around Christmas time (sorry but I can- 1040 members (and they should become more not disclose their names before contacting them by the end of the year!), with approximately 385 and the final approval by the Board). I can only which became members in 2012-2013 for the first anticipate that it will be our way to celebrate the time (or renewed after some years) whereas 115 20th anniversary since the founding of ISBA in members at the end of 2011 did not renew their 1992. membership. We worked hard to get the former members back and we had some success but the In my second failed attempt to become ISBA next ISBA officers should pay a lot of attention to President in the 2008 elections (when Peter Mu- retain members, especially after the recent huge eller was elected), I wrote in my statement the increase, and bring back former ones. The im- sentence “If elected, I promise it will not be a pressive increase has many explanations, like the dull year!”. I do not know your opinion on what World Meeting with discounted rate for mem- happened in ISBA during this year (and I would bers and the creation of new sections, but I hope like to hear from you at [email protected]) that more and more people felt “natural and ob- but, for sure, it has not been a dull year for me. vious”, for a Bayesian, to be an ISBA member. The contact with the members has been a pleasure, and not just a duty towards the owners of We would like that Bayesians will be proud of ISBA (i.e. all of us). I contacted many people for being ISBA members and will be more linked to different reasons (e.g. Latin American summer the society. For those reasons and to properly re- school and Institutional membership), but here cognise those who contribute significantly to the I just want to mention when I asked a hundred development and diffusion of Bayesian ideas, we people to tell me if they had used simple Bayesi- are going to introduce new awards and define an models to address and solve real problems. I better the characteristics of the existing ones (we was expecting just a dozen answers but I got mo- just need a second approval of the bylaws by the re than seventy and people were so enthusiastic Board). We are keeping the awards for young and gave me so many details that it took me ages statisticians to attend meetings (i.e. ISBA New to summarise them into the very long column I

Content 5 www.bayesian.org ISBA Bulletin, 19(4), December 2012 FROM THE PROGRAM COUNCIL wrote for the previous issue of the Bulletin. time to ISBA and contributed a lot in shaping this year’s policy). Finally, I would like to thank the I am very glad of the large number of people members of the Executive Committee (Merlise who took responsibilities this year in organising Clyde, Mike Daniels and Mike Jordan) for their events, proposing sections, being part of commit- support and very friendly cooperation, as well as tees, giving advice and contributing when asked the open and thorough discussions we had and like in the above cases. I believe that ofﬁcers of the joint efforts we made to implement the deci- a society should not limit themselves to decide sions we took within the Exec and the Board. on behalf of its members but they should also activate members’ energies and coordinate them I do not like to get a job just to add a line to my towards a common goal. CV, so I tried to work hard for respect of the role, of the people who elected me, of the members I It has been a great pleasure working with you, have been representing, of myself. Now it is time the ISBA committees and the Board of Directors, to step aside and leave Merlise the responsibili- whose members survived the many, very long ty of leading the society of which I have been a messages I posted in the Board Forum (actually proud President. Auguri a tutti voi. ▲ I have to thank them since they devoted a lot of

AMESSAGEFROMTHE EDITOR for a renewal of the Bulletin Editor ofﬁce, and I would like to take the opportunity to express my deep gratitude to all the Associate Editors who - Manuel Mendoza - have collaborated with us over these years. It is [email protected] only because of their work that the Bulletin ap- pears every quarter. As every December, with the last issue of the year, the ISBA Bulletin witnesses the end of a Let me also welcome Feng Liang who will be- Presidential era and foresees the start of a new come the new Editor, next January. I am sure that one. In this ocasion, the Ruggerian period ap- she will make a great job and we’ll see a bet- proaches its end. It has been a year full of highly ter and more useful Bulletin in the future. As al- productive activity for the Society and Fabrizio ways, I want to encourage all members of ISBA should be congratulated for his successful Pre- to contribute to the Bulletin with their suggesti- sidency. In particular, as Editor of the Bulletin, I ons, manuscripts and announcements. Please do would like to thank Fabrizio for all his support not hesitate to contact any member of the Edito- and guidance. In addition to this change, after rial Board. ▲ three years of enjoyable work, it is now also time

FROM THE PROGRAM COUNCIL

THE INTERNATIONAL YEAR Statisticians, O-Bayes, and Bayes NP) in Italy, OF (BAYESIAN) STATISTICS China, USA, and The Netherlands. There will also be 2 ISBA Chapter meetings (one in India and - Vanja Dukic - another in South Africa) and 7 co-sponsored or [email protected] endorsed meetings in Ireland (Third Symposium on Games and Decisions in Reliability and Risk), Italy (Bayesian Inference in Stochastic Processes 2013, the International Year of Statistics, will be in Milan, and Approximate Bayesian Compu- bustling with Bayesian activities. There will be 4 tation in Rome), Hong Kong (ICSA Internatio- exciting ISBA Section meetings (Bayesian Young nal Conference), USA (Stochastic Processes and

Content 6 www.bayesian.org ISBA Bulletin, 19(4), December 2012 FROM THE BOARD OF DIRECTORS

Their Applications), Spain (Bayesian methods EMS, ENAR, and JSM. The full list of meetings in Biostatistics and Bioinformatics) and Vietnam can be found at bayesian.org. On behalf of the (Statistics and its Interactions with other Disci- ISBA Program Council, we wish all Bayesians a plines). In addition, we will have ISBA-endorsed very Happy New Year! ▲ sessions at several of the major meetings, such as

FROM THE BOARD OF DIRECTORS

SAVE ON ISBA DUES FOR increase to $25. ISBA dues help support Bayesian 2013! Analysis, the Bayes News Forums, travel awards, prizes and more. ISBA membership provides discounts on registration for ISBA conferences, - Merlise Clyde - workshops and continuing education events. ISBA Executive Secretary [email protected] Please visit bayesian.org to join or renew today! Please consider making an unrestricted do- December is renewal month for ISBA annual nation to the ISBA general fund to help support memberships that expire at the end of the year. kick off new ISBA activities or join one of ISBA’s You can save $10 on ISBA dues for 2013 by rene- growing list of sections! New this year, members wing anytime before December 31st. After Janua- may join one of several regional Chapter’s of IS- ry 1 regular ISBA dues will increase to $60, while BA. ▲ student and reduced-country memberships will

INSTITUTIONAL IM is important not only for institutions (espe- MEMBERSHIP cially with the current expansion of ISBA activities and for the advertising possibilities) but also for ISBA, since IM fees could provide a gre- - Fabrizio Ruggeri - at help in supporting the many activities ISBA ISBA President 2012 is promoting. We warmly invite you to contact [email protected] your organisation and promote IM.

The ISBA Board of Directors just approved the Details can be found at Institutional Member- Institutional Membership (IM), offering beneﬁts ship For technical reasons, it is currently possi- to departments, institutions and companies at ble to sign up only as “Organizational Partner”. three different levels (with 50% discount for de- Soon it will be possible to sign up for Standard veloping countries). and Premium IM; an announcement will be done through the Bayes Forum. ▲

Content 7 www.bayesian.org ISBA Bulletin, 19(4), December 2012 2012 ISBA ELECTION

2012 ISBA ELECTION

ISBA 2012 ELECTION Section on Bayesian Nonparametrics RESULTS Chair-Elect Antonio Lijoi, - Merlise Clyde - University of Pavia, Italy, ISBA Executive Secretary [email protected] [email protected] Section on Bayesian Nonparametrics Secretary Surya Tokdar, We are pleased to announce the results of the Duke University, USA, recent ISBA elections (posted at bayesian.org) as [email protected] follows: Section on Finance and Business ISBA President-Elect Chair-Elect Sonia Petrone, Siddhartha Chib, Bocconi University, Milano, Italy, Washington University in St. Louis, USA, [email protected] [email protected] ISBA Executive Secretary Section on Finance and Business Steve Scott, Program Chair Google, USA, Abel Rodriguez, [email protected] University of California, Santa Cruz, USA, [email protected] ISBA Board Paul Fearnhead, Section on Finance and Business Lancaster University, UK, Secretary [email protected] Emily Fox, Amy H. Herring, University of Washington, USA, The University of North Carolina [email protected] at Chapel Hill, USA, amy [email protected] Section on Industrial Statistics Jaeyong Lee, Chair-Elect Seoul National University, South Korea, Ehsan Sooﬁ, [email protected] University of Wisconsin-Milwaukee, USA, Havard˚ Rue, esooﬁ@uwm.edu NTNU, Norway, [email protected] Section on Objective Bayes Program Chair Section on Biostatistics and Pharmacology Susie Bayarri, Chair-Elect University of Valencia, Spain, Sylvia Richardson, [email protected] Medical Research Council Biostatistics Unit and University of Cambridge, Section on Objective Bayes United Kingdom, Treasurer [email protected] James Scott, University of Texas at Austin, USA, [email protected]

Content 8 www.bayesian.org ISBA Bulletin, 19(4), December 2012 SUMMER SCHOOL AND MEETING IN COSTA RICA

On behalf of all ISBA members, we congratu- tributions in coming years! We also again thank late all those named above, thank them for their the candidates who stood for election but were willingness to serve the profession in these posi- not elected (this year!) ▲ tions, and look forward to their leadership con-

SUMMER SCHOOL AND MEETING IN COSTA RICA

NEWSFROM LATIN AMERICA tisticians and outstanding Bayesian researchers which would be hardly possible otherwise and creating a network of young people from diffe- - Fabrizio Ruggeri - rent countries which could cooperate in future ISBA President 2012 in scientific works and organisation of further [email protected] events. ISBA is investing a lot on the project by partially supporting many young people (and I am glad to inform you that the Universidad donations to ISBA to support these activities are de Costa Rica will host the first “Latin Ameri- always welcome!). can Summer School in Bayesian Statistics” (name suggested by my one-time consultant for English In January we will announce details on the language, Michael Jordan, who proposed also meeting, the school and the travel grants through the short name “LA-Bayes”). The school will be the Bayes Forum operated by ISBA. In the mean- held in San Jose´ on July, 22-24, 2013 and it will be while, Luis Raul and myself will work on the followed by a two-days Bayesian meeting and, international side of the invited programme (we probably, an excursion on July, 27th. hope to get many people) and Edgar Gutierrez´ and Eiliana Montero, the local hosts, will work The lecturers will be Raquel Prado (University on the organisation of the events, invitation of of California at Santa Cruz) and Luis Raul Peric- people from Costa Rica and website. chi (University of Puerto Rico); Luis Raul should give an introduction to Bayesian statistics whe- If you are interested in attending the school, reas Raquel should talk about time series. This giving a talk or presenting a poster (slides and will be the first LA-Bayes school to be followed posters, if any, in English will be allowed!), plea- by one in Mexico in 2014 and one in Colombia in se send me a message to [email protected] 2015, just before ISBA 2014 and COBAL4, respec- (later there will be an ad-hoc e-mail address for tively. The official language of the 2013 school the events). and meeting will be Spanish since we would like to favour the participation of the largest number P.S. Latest news. The list of speakers at the mee- of students and young (and less young ...) re- ting will include Raquel Prado, Luis Raul Peric- searchers from an area where Bayesian methods chi, Carlos Pereira, Alicia Carriquiry, Abel Rod- are hardly taught. The Latin American summer riguez, Rosangela Loschi, Elias Moreno, Carlos school has the goal to promote the diffusion of Barrera, Gabriel Huerta, Andres Christen, Manu- Bayesian statistics in the continent, especially el Mendoza and others who have to confirm. ▲ allowing for contacts between local young sta-

Content 9 www.bayesian.org ISBA Bulletin, 19(4), December 2012 BAYESIAN ANALYSIS - A MESSAGE FROM THE EDITOR

BAYESIAN ANALYSIS - A MESSAGE FROM THE EDITOR

UPDATE FROM BA and effort, sometimes on short notice, to make it all happen. Our board of editors makes the re- - Herbie Lee - view process run: Ming-Hui Chen, Kate Cowles, Editor-in-Chief David Dunson, David Heckerman, Valen John- [email protected] son, Antonietta Mira, Sonia Petrone, Bruno San- so, Mark Steel, and Kert Viele, as well as Michael It’s hard to believe that three years have alrea- Jordan and Fabrizio Ruggeri who were also on dy passed, but my term as editor is drawing to a the board in the first part of this period. close. I am leaving the journal in excellent hands, as Marina Vannucci is taking over as Editor-in- The editors are supported by a larger num- Chief. Our submissions are up and I am happy ber of associated editors and a vast number of to be able to leave the journal in good health to referees. Thank you to all of you who have con- Marina. Two big pieces of news for the journal tributed, and thank you to ISBA for giving me during this time are the move to Project Euclid the opportunity to lead this great journal. Whi- (find us at projecteuclid.org) and the move to a le we will be sad to see Alyson Wilson stepping new online review system, EJMS, which is sha- down, we are happy to welcome Kassie Fron- red with the IMS journals (this move is still in czyk as the incoming Managing Editor. Alyson progress as I write, but we should be going live has done a great job, so Kassie has a hard act to very soon). I am grateful to Merlise Clyde for all follow, but I think she will be up to the task. We her help in moving us to Project Euclid. Another look forward to great success from the Marina- rite of passage for the journal was receiving our Kassie team, along with Pantelis and Kary who first impact factor, thanks to the work of the pre- will be continuing. vious EIC Brad Carlin. We have scored very well on article influence and our 5-year impact factor. Finally, I do want to mention that we have another great issue in the December 2012 issue. The Bayesian Analysis is a journal that survives on discussion paper is a case study on human fe- the hard work of a large team of volunteers. I am cundity by Sungduk Kim, Rajeshwari Sundaram, immensely thankful for everyone who pitches Germaine M. Buck Louis and Cecilia Pyper, with in. Critical to our success are the Managing Edi- discussions from Bruno Scarpa and Joseph Stan- tor Alyson Wilson, the System Managing Editor ford. We have a big issue (and our first volume Pantelis Vlachos, and the Production Editor Kary over one thousand pages) with a variety of other Myers (and Angelika van der Linde before her). primarily methodological papers including non- These people put in significant amounts of time parametric modeling and robust modeling. ▲

ISBA - SECTIONS

BAYESIAN COMPUTATION Mira, Havard˚ Rue, Nicolas Chopin and myself. SECTION We are delighted by the enthusiasm shown for this new initiative, in particular by the 115 mem- - Peter J. Green - bers (at the time of writing) from 21 countries Chair who have already signed up to join the section. [email protected] But 115 is not our limit and we hope for many more to sign up. Elections for ofﬁcers were held The gestation period of the new BayesComp in early December, and so we now have a com- section has been guided by an informal steering plete set of ofﬁcers: group, consisting of Christian Robert, Antonietta

Content 10 www.bayesian.org ISBA Bulletin, 19(4), December 2012 ISBA - SECTIONS

Section Chair, to end 2013 We are actively planning our ﬁrst big event, Peter Green, MCMSki IV, in Chamonix-Mont Blanc, France [email protected] from 6-8 January 2014, and the plenary speakers are now conﬁrmed as Andrew Gelman (Colum- Program Chair, to end 2013 bia University, New York), Chris Holmes (Uni- versity of Oxford), and Michele Parrinello (USI, Christian Robert, Lugano and ETH Zurich).¨ Make sure you use the [email protected] 2013 ski season to get in practice for this conference! Secretary, to end 2014 Antonietta Mira, Finally, in our “manifesto” for the Section, we [email protected] promised a “website of information, tools, and advice as an authoritative central resource for Treasurer, to end 2014 Bayesian computation”. We are actively working Galin Jones, on our plans for this, and will go public with the- [email protected] se soon. In the meantime, I welcome your ideas for what this might include: please be creative in Section Chair-elect, to end 2013 your suggestions, but also generous with your Section Chair, 2014-2015 time: ideas for labour-intensive features on the website will be particularly welcome if accompa- Havard˚ Rue, nied by an offer to construct and maintain! ▲ [email protected]

ECONOMICS,FINANCE term); Emily Fox, EFaB Secretary in 2013-2014 ANDBUSINESSSECTION (two year term). If you have not already done so, please join me in congratulating the new officers, - Mike West - and helping them understand that we expect a Chair great deal from them in the coming two years! [email protected] I would also like to again thank all other candidates this year– Mike So, Carlos Carvalho, and The ISBA Section on Economics, Finance and Hongxia Yang– for their commitments and inte- Business (EFaB) aims to promote, encourage and rests in running for office, and to remind them reflect the vitality of Bayesian methods in appli- that there will be continuing opportunities! cations across the full spectrum of commercial, financial and economic areas. In this issue of the Education & Outreach: We would like to in- Bulletin, the first piece of news for ISBA members vite all EFaB members to consider volunteering broadly– as well as EFaB members in particular– to contribute to EFaB’s developing short-course is that the ISBA Board formally approved the re- initiatives. In early 2013 we will put together a vised section name recently (to add the “E”). The formal Continuing Education Committee as an ex- Section’s purview is the full sweep of Bayesian tension of the executive committee, drawing on analysis in all areas of economics, finance and the membership, of course. Beyond the formali- business. ties and developing blueprints and logistics, we are interested in hearing from the membership of Elections: As you will all already know, the an- EFaB. Two of our three central goals are to pro- nual ISBA elections ended with the following ne- mote education in Bayesian methods in finance and wfaces elected to lead and develop EFaB on be- business by developing short-courses for students and half of the members. From January 1st 2013, our practitioners; and (to) promote academic-industry in- Executive Committee is completed with the ad- teractions and outreach to the finance and business dition of: Siddhartha Chib, EFaB Section Chair- professions. We now solicit: (i) ideas and suggesti- elect for 2013, Chair in 2014; Abel Rodriguez, ons for topics and speakers for short courses (ran- EFaB Program Chair in 2013-2014 (two year ging from 1- or 2-day courses, to “collages” of

Content 11 www.bayesian.org ISBA Bulletin, 19(4), December 2012 ISBA - SECTIONS

3-4 speakers/teachers for one full day together, sting and time series analysis, with applica- to tutorial-style and master-class presentations); tions in EFaB areas. Several EFaB members and (ii) ideas and suggestions for venues– free- are involved in organisation and as invited standing, academic, commercial, in-house or col- speakers, and the call for contributed pre- laborative with other organisations (whether so- sentations is open until January 31, 2013. cietal, business, academic, etc), that might be EFaB members are encouraged to partici- imagined as defining contexts for initial short- pate and we hope and expect to enjoy a sti- courses that would then evolve into “series” of mulating and eventful meeting, the first of continuing events. Courses (master classes, tuto- what is expected to be a new series of inter- rials, or more specific topic-oriented courses) re- national workshops on time series methods sponding to articulated interests of other groups, and applications. business or economic organisations, etc., are of particular interest. • RCEA-BEW7, the 7th Annual Bayesian Eco- If you are interested in discussing the abo- nometric Workshop of the Rimini Centre for ve, participating, volunteering, (volunteering Economic Analysis. RCEA is an Italian eco- others), and/or have any other input, please do nomic research centre with strong links to not hesitate to come forward to help with these Canadian economists, and has a growing central EFaB initiatives. You can to this by emai- Bayesian econometrics group that, among ling any one of the current executive committee other activities, has an annual workshop members, and maybe most directly discussing and is active in encouraging participation with me, as current EFaB Chair, and/or Abel Ro- of junior Bayesian econometricians. On be- driguez, as EFaB Program Chair beginning on Ja- half of ISBA, EFaB is officially endorsing nuary 1st 2013. RCEA-BEW7. The meeting is in Rimini, Ita- ly, on June 25-26, 2013, and will focus on the broad range of topics in Bayesian econome- Meetings in 2013: EFaB formally endorses or trics. Several EFaB members are involved in sponsors workshops and conferences concerned organisation and as invited speakers at the wholly or substantially with Bayesian ideas, me- meeting. The full workshop announcement thods and applications in the “E”, “F” and “B” and call for contributed presentations will areas. All members are encouraged to come for- be available very soon, and we will advi- ward with ideas and proposals for endorsement se EFaB members via email once details are and/or sponsorship of meetings. available at the RCEA web site. We are currently discussing/finalizing formal EFaB endorsement of several meetings, and will • ESOBE 2013, the 2013 meeting of the announce details (via the ISBA email lists as well European Seminar on Bayesian Econometrics as forthcoming issues of the Bulletin) as they co- (ESOBE), a discussion forum for novel and me on stream. Some of these are expected to in- recent research in a wide range of topics volve short-course activities of direct interest to in the field of Bayesian econometrics. On EFaB members and Bayesians working in these behalf of ISBA, EFaB is officially endor- areas, and EFaB sponsorship as well as endorsing ESOBE 2013 as part of a developing sement. Of key interest to our members is the relationship involving discussions of po- news that, in some cases, the endorsement agree- tential broader collaborations with ESOBE. ment will involve reduced registration fees for IS- The ESOBE 2013 meeting will be hosted by BA/EFaB members. the Norges Bank in Oslo on August 22-23, By way of initial news about EFaB meeting en- 2013. The program will include a rich mix dorsements for 2013, we are pleased to announce of keynotes and special invited sessions, that EFaB endorses the following three meetings. with opportunities for EFaB members to present talks and/or posters; the meeting • Time Series 2013, the 1st Vienna Workshop scope spans the field of Bayesian methods on High Dimensional Time Series in Macroeco- in econometrics and related areas. Several nomics and Finance, to be held in (you gues- EFaB members are involved in organisation sed it!) Vienna in May 2013. On behalf of of the meeting. The conference web site will ISBA, EFaB is officially endorsing Time Se- be “up” before the end of December, and ries 2013. The meeting will focus on factor we will advise EFaB members via email as models and Bayesian methods for foreca- soon as it is available. The call for papers

Content 12 www.bayesian.org ISBA Bulletin, 19(4), December 2012 ISBA - SECTIONS

will have a deadline of April 1, 2013. EFaB@Bayes 250 Program Committee with more details. This EFaB meeting will be run in coor- We are also expecting that ISBA/EFaB dination with ISBA and also the ISBA/Objective members will receive a modest discount on Bayes section who will be running a parallel mee- conference fees, to be announced later on. ting bracketing Bayes 250. EFaB Program Chair EFaB members are encouraged to partici- (2013-14) Abel Rodriguez is leading this, as chair pate in what will surely be a stimulating of the EFaB@Bayes 250 Workshop Committee. and eventful meeting on frontier research in methodology and applications of Baye- sian methods in econometrics and related We invite and encourage all ISBA members to areas. contact any of us to discuss ideas for EFaB activities of any kind (consistent with the Secti- on aims and bylaws), and especially related to More Meetings in 2013: EFaB@Bayes 250! As short-courses, workshops and conferences linked announced in the previous Bulletin, all Bayesians to other groups in any areas of business and ﬁ- should be encouraged to take particular note of nance, and other forms of outreach. Please visit events and activities at Duke University in mid- the Section web page at the ISBA site. December 2013: Bayes 250!. To mark and celebra- In closing, I probably do not need to remind all te the 250th anniversary of the formal reading of 1-year EFaB members to renew section member- Bayes’ seminal paper to the Royal Society, ISBA ship when renewing with ISBA for the coming will host the Bayes 250 meeting at Duke Univer- year(s) .... but will do so: don’t forget to renew! And sity during the 3rd week of December 2013, and all ISBA members not currently involved with also highlight it in connection with the Interna- EFaB are encouraged to join the Section– you can tional Year of Statistics 2013. do this by logging into your ISBA membership As part of this, we will have an EFaB mee- account and simply adding the Section member- ting during the 2 days before formal Bayes 250 ship (either annual or life), or directly via the Sec- talks; the EFaB@Bayes 250 Workshop is schedu- tion page. Please tell your friends and colleagues, led for December 15-16, 2013. This EFaB meeting and help us to develop the Section to promote, will include tutorial/short course activities along facilitate and celebrate Bayesian analysis in eco- with research talks, and be consistent with EFaB’s nomics, ﬁnance and business. aims of promoting cross-over between academic With good wishes for the holiday season and and non-academic research, coupled with educa- for a productive, successful and enjoyable Baye- tion and outreach. Mark your calendars and make sian New Year 2013, pre-holiday travel plans! We hope and expect to see a major representation of EFaB members at Duke With best regards, University next December. In the next few weeks, you will hear from the Mike West ▲

NONPARAMETRICS will be taking over in January. I would like to ta- SECTION ke this opportunity to personally thank all those who have helped out on the committee during - Stephen G. Walker - this time: Maria Kalli, Ramses Mena, Theo Nico- Chair leris, Thanos Kottas, Michele Guindani and Steve [email protected] himself.

This will be the ﬁnal message from me as the I wish all the future committees the very best Nonparametric Section chair. Steve MacEachern and may Bayes nonparametrics ﬂourish. ▲

Content 13 www.bayesian.org ISBA Bulletin, 19(4), December 2012 SOFTWARE HIGHLIGHT

JUNIORSECTION Statistics, to discuss and share ideas and projects with the Bayesian community at large. Social - Andrew Cron - events are also planned, in order to let people Chair have fun together and create useful networks for [email protected] their future work and career. In order to encoura- We are pleased to announce that the Junior IS- ge participation and submissions, registration is BA section has been launched and now has over FREE. Works can be submitted by PhD students, 40 members! We hope to see that number incre- post-docs and MS students with outstanding the- ase over the coming year (it is possible to join ses/projects in Bayesian Statistics and will be pu- us when renewing the ISBA membership), also blished in an extended proceeding book after the thanks to the number of initiatives the section is conference. preparing (MAYBE BETTER ANOTHER TERM). In fact, we have multiple conference events this We are also organizing a session at GDRR 2013: coming year, and we are planning to do multiple Third Symposium on Games and Decisions in web-based events as well. Reliability and Risk on July 8th-10th in Kinsale, Ireland (www.cs.tcd.ie). The objective of the sym- We are collaborating with the Bayesian Non- posium is to present novel use of game and deci- parametrics Section in order to have a couple sion theory in reliability and risk analysis and to of events dedicated to junior researchers at their bring together researchers from disciplines such next conference in Amsterdam on June 10-14, as economics, engineering, ﬁnance, mathematics, 2013 (www.bnp9.win.tue.nl). In particular, a pri- medical sciences, probability and statistics who ze will be awarded for best poster submitted by have a lot to contribute to this theme. There will a junior researcher, and a lunch event will be ho- be a call for abstracts and selected works by ju- sted speciﬁcally for participating junior statisti- nior researchers will be selected to present in the cians. Stay tuned for more details on the confe- session and for travel support. rence website and in an email to ISBA members. We are also endorsing and supporting the Please visit the J-ISBA website for more infor- BAYSM 2013 - Bayesian Young Statistician mation, be on the lookout for an email to the Meeting on June 5th and 6th in Milan, Italy members for more information and stay tuned (www.mi.imati.cnr.it). The meeting is devoted for more information about upcoming events. ▲ to let young researchers, dealing with Bayesian If you haven’t already, join J-ISBA!

SOFTWARE HIGHLIGHT

CONTINUOUS DOMAIN SPATIAL tial equations (SPDEs), and write down explicit MODELSIN R-INLA links between the parameters of each SPDE and the elements of precision matrices for weights - Finn Lindgren - in a discrete basis function representation. As [email protected] shown by Whittle in 1963, such models include those with Matern´ covariance functions, which are ubiquitous in traditional spatial statistics, but Traditionally, Markov models in image analy- in contrast to covariance based models it is far ea- sis and spatial statistics have been largely confi- sier to introduce non-stationarity into the SPDE ned to discrete spatial domains, such as lattices models. This is because the differential opera- and regional adjacency graphs. However, as dis- tors act locally, similarly to local increments in cussed in Lingren et al. (2011), one can express a Gibbs-specifications of Markov models, and on- large class of random field models as solutions ly mild regularity conditions are required. The to continuous domain stochastic partial differen- practical significance of this is that we can mer-

Content 14 www.bayesian.org ISBA Bulletin, 19(4), December 2012 SOFTWARE HIGHLIGHT ge the classical Gaussian random fields with me- The simplest model for x(s) currently imple- thods based on the Markov property, providing mented in R-INLA is the SPDE/GMRF version of continuous domain models that are computatio- the stationary Matern´ family, nally efficient, and where the parameters can be (κ2 − ∆)α/2(τx(s)) = E(s), s ∈ 2, specified locally without having to worry about R positive definiteness of covariance functions. where ∆ is the Laplacian, κ is the spatial scale parameter, α controls the smoothness of the rea- In this brief note, I present the basic ingredients lisations, and τ controls the variance. The right- of the link between continuous domains and hand side of the equation, E(s) is spatial white Markov models, and show how to perform Baye- noise process. The link to the Matern´ smooth- sian inference for the simplest of these models, ness ν and variance σ2 is ν = α − d/2 and σ2 = using the R-INLA software package (http://www. Γ(ν)(Γ(α)(4π)d/2κ2ν τ 2)−1, where d is the spati- r-inla.org). Special emphasis is placed on the al dimension. From this we can identify the ex- abstractions necessary to simplify the practical ponential covariance with ν = 1/2 and α = 3/2, bookkeeping for the user of the software. and note that fields with α ≤ 1 give ν ≤ 0 and that such fields have no point-wise interpretati- on (but do have well-defined integration properties). From spectral theory one can show that in- Think continuous teger values for α gives continuous domain Mar- kov fields, and these are the easiest for which to provide discrete basis representations. In R-INLA, When building and using hierarchical models the default value is α = 2, but 0 ≤ α < 2 are with latent random fields it is important to re- also available, though not as extensively tested member that the latent fields often represent real- (for the non-integer α values the approximation world phenomena that exist independently of method introduced in the authors’ discussion re- whether they are observed in a given location or sponse in Lingren et al. (2011) is used). not. Thus, we are not building models solely for discretely observed data, but for approximations of The models discussed in Lingren et al. (2011) entire processes defined on continuous domains. and implemented in R-INLA are built on a basis For a spatial field x(s), while the data likelihood representation typically depends only on the values at a finite n set of locations, {s ,..., s }, the model itself de- X 1 m x(s) = ψ (s)x , fines the joint behaviour for all locations, typical- i i i=1 ly s ∈ R2 or s ∈ S2 (a sphere/globe). In the case of lattice data, the discretisation typically hap- where the joint distribution of x = {x1, . . . , xn} pens in the observation stage, such as integrati- is chosen so that the distribution of the function over grid boxes (e.g. photon collection in a ons x(s) approximates the distribution of soluti- camera sensor). Often, this is approximated by ons to the SPDE. To obtain a Markov structure, point-wise evaluation, but there is nothing apart and to preserve it when conditioning on obser- from computational challenges preventing other vations, we use basis function with local support. observation models. The construction is done by projecting the SPDE onto the basis representation in what is essenti- As discussed in the introduction, an alternati- ally a Finite Element method. To allow easy and ve to traditional covariance based modelling is explicit evaluation, we use piece-wise linear ba- to use SPDEs, but carry out the practical com- sis functions defined by a triangulation of the do- putations using Gaussian Markov random field main of interest. This yields a diagonal matrix C (GMRF) representations. This is done by appro- and a sparse matrix G such that the appropriate ximating the full set of spatial random functions precision matrix for the weights is given by with weighted sums of simple basis functions, Q = τ 2(κ4C + 2κ2G + GC−1G) which allows us to hold on to the continuous in- terpretation of space, while the computational al- for the default case α = 2, so that the elements of gorithms only see discrete structures with Mar- Q have explicit expressions as functions of κ and kov properties. Beyond the main paper Lingren τ. The default internal representation of the pa- et al. (2011), this is further discussed in Simpson rameters in the model interface we will use here et al. (2012a) and (2012b). is log(τ) = θ1 and log(κ) = θ2, where θ1 and θ2

Content 15 www.bayesian.org ISBA Bulletin, 19(4), December 2012 SOFTWARE HIGHLIGHT have a joint normal prior distribution (by default points = matrix(runif(m*2),m,2) independent). mesh = inla.mesh.create.helper( points=points, There is a vast range of possible extensions cutoff=0.05, to the simple model described here, including offset=c(0.1,0.4), non-stationary versions (see Lingren et al. (2011) max.edge=c(0.05,0.5) ) and Bolin & Lindgren (2011) for examples). For plot(mesh) currently implemented models, the recent paper points(points[,1],points[,2]) Cameletti et al. (2012) is a case-study using a The cutoff parameter is used to avoid building straightforward space-time version including the many small triangles around clustered input lo- full R code. A non-stationary extension by defi- cations, offset specifies the size of the inner and ning spatially varying models for κ(s) and τ(s) is outer extensions around the data locations, and also implemented, and will be mentioned briefly max.edge specifies the maximum allowed trian- later on. gle edge lengths in the inner domain and in the outer extension. The overall effect of the triangu- While the full theory behind fractional stocha- lation construction is that, if desired, one can ha- stic partial differential equations is challenging at ve smaller triangles, and hence higher accuracy best, the major challenge when designing a ge- of the field representation, where the observation neral software package for practical use of the- locations are dense, larger triangles where data se models is rather that of bookkeeping. To solve is more sparse (and hence provides less detailed this, a bit of abstraction is needed to avoid clut- information), and large triangles where there is tering the interface with details of internal stora- no data and spending computational resources ge. Thus, instead of visibly keeping track of map- would be wasteful. However, note that there is pings between triangle mesh node indices and neither any guarantee nor any requirement that data locations, one can use sparse matrices to en- the observation locations are included as nodes code these relationships, and provide wrapper in the mesh. If one so desires, the mesh can be functions to manipulate these matrices and asso- designed from different principles, such as latti- ciated index and covariate vectors. ce points with no relation to the precise measure- The first step is to create the triangulated mesh ment locations. This emphasises the decoupling on top of which the SPDE/GMRF representation between the continuous domain of the field mo- is to be built. The example here illustrates a com- del and the discrete data locations. mon usage case, which is to have semi-randomly scattered observation locations in a region of Defining an SPDE model object can now be as space such that there is no physical boundary, simple as just a limited observation region. When dealing spde=inla.spde2.matern(mesh,alpha=2) with only covariances between data points, this distinction is often unimportant, but here it beco- but in practice we need to also specify the prior mes a possibly vital part of the model, since the distribution for the parameters, and/or modify SPDE will exhibit boundary effects. In the R-INLA the parameterisation to suit the specific situati- implementation, Neumann boundaries are used, on. This is true in particular when the models are which increases the variance near the boundary. used as simple smoothers, as there is then rare- If we intend to model a stationary field across the entire domain of observations, we must therefore ly enough information in the likelihood to fully extend the model domain far enough so that the identify the parameters, giving more importance boundary effects do not influence the observati- to the prior distributions. ons. However, note that the reverse is also true: if √ there is a physical boundary, the boundary effects The empirically derived expression 8ν/κ can may actually be desirable. The helper function be used as a measure of the spatial range of the inla.mesh.create.helper() allows us to crea- model, which allows us to construct a model with te a mesh with small triangles in the domain of known range and variance for (θ1, θ2) = (0, 0), via interest, and use larger triangles in the extension used to avoid boundary effects. This minimises sigma0 = 1 the extra computational work needed due to the range0 = 0.2 extension. kappa0 = sqrt(8)/range0 tau0 = 1/(sqrt(4*pi)*kappa0*sigma0) m = 100 spde=inla.spde2.matern(mesh,

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B.tau=cbind(log(tau0),1,0), Here, the inla.mesh.project/or() functions B.kappa=cbind(log(kappa0),0,1), are used to map between the basis function theta.prior.prec=1) weights for the mesh nodes and a lattice format more suited to the standard plotting routines, by Here, B.tau and B.kappa can be generalised into default a 100 × 100 lattice covering the mesh do- matrices where the first column specifies a spati- main. ally varying offset for log(τ) and log(κ), and the other columns specify basis functions, together defining a non-stationary SPDE model with parameters given by the log-linear models Bayesian inference

p X We will now look at a simple example of how to log(τ(s)) = bτ (s) + bτ (s)θ 0 k k use the SPDE models in latent Gaussian models k=1 when doing direct Bayesian inference based on p integrated nested Laplace approximations as in- κ X κ log(κ(s)) = b0 (s) + bk (s)θk troduced in Rue et al. (2009). k=1 Let us consider a simple Gaussian linear model where B· = b· (s ), with the columns indexed ik k i involving two independent realisations (replica- from 0 and s are the locations of the mesh no- i tes) of a latent spatial field x(s), observed at the des. Setting sensible priors for θ in these models same m locations, {s1,..., sm}, for each replicate. in general is beyond the scope of this note, and For each i = 1, . . . , m, the default priors in the package are likely to change in the near future as we gain more ex- yi = β0 + ciβc + x1(si) + ei, perience with their behaviour, in particular for y = β + c β + x (s ) + e , non-stationary models. The model defined here i+m 0 i+m c 2 i i+m will give an approximate prior mean variance of where ci is an observation-specific covariate, ei is σ2 = 1 for the field, and approximate prior mean 0 measurement noise, and x1(·) and x2(·) are the range 0.2 with a prior variance for the range dis- two field replicates. Note that the offset, β0, can tribution to reach the size of the domain, but not be interpreted as a spatial covariate effect, con- very far beyond. stant over the domain.

Models with range larger than the domain We use the basis function representation of size are usually indistinguishable from intrin- x(·) to define a sparse matrix of weights A P sic random fields, which can be modelled by such that x(si) = j Aijxj, where {xj} is the fixing κ to zero (or rather some small positi- joint set of weights for the two replicate fields. ve value) with B.tau=cbind(log(tau0),1) and If we only had one replicate, we would have B.kappa=cbind(log(small),0). Note that the Aij = ψj(si). The matrix can be generated by sum-to-zero constraints often used for lattice ba- inla.spde.make.A(), which locates the points in sed intrinsic Markov models are inappropriate the mesh and organises the evaluated values of due to the irregular mesh structure, and a weigh- the basis functions for the two replicates: ted sum-to-zero constraint is needed to reprodu- A=inla.spde.make.A( ce such models. A future version of the softwa- mesh, re will include an automatic option to construct loc=points, such appropriate constraints. index=rep(1:m,times=2), repl=rep(1:2,each=m) ) Helper functions in the package can produce precision matrices for given parameter values, as For each observation, index gives the correspon- well as samples, so we can generate a synthetic ding index into the matrix of measurement lo- sample: cations, and repl determines the corresponding Q=inla.spde2.precision( replicate index. In case of missing observations, spde,theta=c(0,0)) one can either keep this A-matrix while setting x=as.vector(inla.qsample(n=1,Q)) the corresponding elements of the data vector y proj = inla.mesh.projector(mesh) to NA, or omit the corresponding elements from image(inla.mesh.project( y as well as from the index and repl parameters proj,field=x)) above. Also note that the row-sums of A are 1,

Content 17 www.bayesian.org ISBA Bulletin, 19(4), December 2012 SOFTWARE HIGHLIGHT

since the piece-wise linear basis functions we use weight matrices, and effects and joins them, ad- sum to 1 at each location. ding NA where needed. Identity matrices and constant covariates can be abbreviated to scalars, Rewriting the observation model on vector with a complaint being issued if the input is inform gives consistent or ambiguous.

y = 1β0 + cβc + Ax + e We also need to keep track of the two ﬁeld rep- = A(x + 1β0) + cβc + e licates, and use inla.spde.make.index(), which gives a list of index vectors for indexing the full Using the helper functions, we can generate a mesh and its replicates (it can also be used for synthetic sample from our model for the latent indexing Kronecker product group models, e.g. ﬁelds and observations: in simple multivariate and spatio-temporal models). The code Q=inla.spde.precision( spde,theta=c(0,0)) mesh.index=inla.spde.make.index( x=as.vector(inla.qsample(n=2,Q)) name="field", covariate = rnorm(m*2) n.mesh=mesh$n, n.repl=2) y = 5 + covariate*2 + as.vector(A %*% x) + generates a list mesh.index with three index vec- rnorm(m*2)*0.01 tors,

The formula in inla() defines a linear predic- field = (1, . . . , n, 1, . . . , n), tor η as the sum of all effects, and a NA in a cova- field.repl = (1,..., 1, 2,..., 2), riate or index vector is interpreted as no effect. To = (1,..., 1, 1,..., 1). accommodate predictors that involve more than field.group one element of a random effect, one can specify The predictor information for the observed data a sparse matrix of weights defining an arbitrary can now be collected, using linear combination of the elements of η, giving a new predictor vector η∗. The linear predictor st.est=inla.stack( output from inla() then contains the joint vec- data=list(y=y), A=list(A,1), tor (η∗, η). To implement our model, we separate effects=list( the spatial effects from the covariate by defining c(mesh.index,list(offset=1)), list(cov=covariate)), x + 1β0 ηe = , tag="est") cβc Each “A” matrix must have an associated list and construct the predictor as of “effects”, in this case A:(field, field.repl, ∗ field.group, offset) and 1:(cov). The data ηe = A(x + 1β0) + cβc list may contain anything associated with the = AI η e “left hand side” of the model, such as expos- = Aeηe ure E for Poisson likelihoods. By default, du- ∗ plicates in the effects are identified and repla- so that now E(y|ηe) = η . The bookkeeping re- e ced by single copies (compress=TRUE), and ef- quired to describe this to inla() involves conca- fects that do not affect η∗ are removed comple- tenating matrices and adding NA elements to the tely (remove.unused=TRUE), so that each column covariates and index vectors: of the resulting A matrix has a least one non-zero Ae = AI2m element. field0 = (1, . . . , n, 1, . . . , n) If we want to obtain the posterior prediction of field = (field0, NA,..., NA) the combined spatial effects at the mesh nodes, offset = (1,..., 1, NA,..., NA) x(si) + β0, we can define

cov = (NA,..., NA, c1, . . . , c2m) ηp = x + 1β0 ∗ Doing this by hand with cBind(), c(), and ηp = Iηp = Apηp rep() quickly becomes tedious and error-prone, so one can instead use the helper function inla.stack(), which takes blocks of data, and construct the corresponding information stack with

Content 18 www.bayesian.org ISBA Bulletin, 19(4), December 2012 SOFTWARE HIGHLIGHT st.pred=inla.stack( to extract the relevant bits and transform them data=list(y=NA), into more user-friendly information, such as po- A=list(1), steriors for range and variance instead of raw effects=list( distributions for θ: c(mesh.index,list(offset=1))), tag="pred") result = inla.spde2.result( inla.result, "field", spde) We can now join the estimation and prediction plot(result[ stack into a single stack, "marginals.range.nominal"][[1]]) stack = inla.stack(st.est,st.pred) The posterior means and standard deviations for This stacks the information, and simplifies the re- the latent fields can be extracted and plotted sult by removing duplicated effects: as follows, where inla.stack.index() provides the necessary mappings between the inla() out- ∗ Ae 0 ηe ηs = put and the original data stack specifications: 0 Ap ηp   index=inla.stack.index( x + 1β0 A I 0 stack,"pred")$data =  cβc  0 0 I image(inla.mesh.project(proj, x + 1β0 inla.result[[ AI x + 1β = 0 "summary.linear.predictor" I 0 cβc ]]$mean[

= Asηs index[mesh.index$field.repl==1]])) In this simple example, the second block row of As a ﬁnal note, the R-INLA package is in con- As (generating x + 1β0) is not strictly needed, sin- stant development, with new models added as ce the same information would be available in ηs they are needed and developed. The current itself if we speciﬁed remove.unused=FALSE when work for the SPDE models is focusing on comple- constructing stack.pred and stack, but in gene- ting the documentation, as well as tying together ral such special cases can be hard to keep track the last bits of the interface for one-dimensional of. models and simple space-time models. Most of the code for this is already in place, but still in We are now ready to do the actual estimation. a slightly esoteric form. Also in the pipeline is a Note that we must explicitly remove the default separate package for computing level excursion intercept from the η-model, since that would otherwise be applied twice in the construction of sets with joint excursion probabilities, as well as η∗, and the constant covariate offset is used in- contour uncertainty regions, mainly developed stead: by David Bolin. formula = y ~ -1 + offset + cov + f(field, model=spde, Acknowledgements replicate=field.repl) inla.result = inla(formula, I want to thank my collaborators David Bolin, data=inla.stack.data(stack), Michela Cameletti, Peter Guttorp, Janine Illian, family="normal", Johan Lindstrom,¨ Daniel Simpson, and last but control.predictor= not least Havard˚ Rue, who is also the main de- list(A=inla.stack.A(stack), veloper of R-INLA. I am also grateful to the IS- compute=TRUE)) BA Bulletin editors for providing this opportuni- The function inla.stack.data() produces the ty to discuss the SPDE/GMRF part of the R-INLA list of variables needed to evaluate the formu- software, and giving me a chance to climb onto a la (use inla.stack.data(stack)$E to extract few, though arguably diminutive, soap-boxes re- the Poisson exposures mentioned earlier) and garding spatial modelling philosophy. inla.stack.A() extracts the A matrix. s The R-code from this note is available at http: Since the SPDE-related contents of //people.bath.ac.uk/fl353/isba/isbaspde. inla.result can be hard to interpret, the hel- R, including code for generating more appealing per function inla.spde2.result() can be used images than the image() function provides.

Content 19 www.bayesian.org ISBA Bulletin, 19(4), December 2012 NEWS FROM THE WORLD

[2] Cameletti, M., Lindgren, F., Simpson, D. and Rue, H. (2012). Spatio-temporal modeling of par- 8 ticulate matter concentration through the SPDE approach, AStA Advances in Statistical Analysis, in

7 press. Case study code available on http://www. r-inla.org.

6 [3] Lindgren, F., Rue, H. and Lindstrom,¨ J. (2011). An explicit link between Gaussian ﬁelds and 5 Gaussian Markov random ﬁelds: the stochastic partial differential equation approach (with dis- 4 cussion), Journal of the Royal Statistical Society, Se- ries B, 73, Part 4, pp. 423–498. 3 [4] Rue, H., Martino, S. and Chopin, N. 2 (2009). Approximate Bayesian Inference for La- tent Gaussian Models Using Integrated Nested Laplace Approximations (with discussion), Jour- nal of the Royal Statistical Society, Series B, 71, pp. Figure 1: Posterior mean 319–392.

[5] Simpson, D., Lindgren, F. and Rue, H. (2012a). References Think continuous: Markovian Gaussian models in spatial statistics, Spatial Statistics, 1, pp. 16–29. [1] Bolin,D. and Lindgren, F. (2011). Spatial mo- [6] Simpson, D., Lindgren, F. and Rue, H. (2012b). dels generated by nested stochastic partial diffe- In order to make spatial statistics computational- rential equations, with an application to global ly feasible, we need to forget about the covarian- ozone mapping, Annals of Applied Statistics, 5, pp. ce function, Environmetrics, 23(1), pp. 65–74. ▲ 523–550.

NEWS FROM THE WORLD

Announcements is intended to expand the knowledge of theory, application of mathematical finance as well 2014 ISBA World Meeting as to enhance the interchange of understandings between academics and practitioners of mathe- Stay tuned! ISBA2014 will be coming to Cancun, matical finance in its variety of spins and flavors Mexico!´ Tentative dates are July 14-18, so be sure as it applies to application of mathematics, nu- to block your calendar. merical methods and statistics to financial issues.

The conference is expected to include experts Meetings and conferences from both academia and industry talking on sub- jects relevant to models as well as solutions to existing and developing models. The conference International Conference on Mathematical Fi- is expected to consist predominantly of multiple nance, Miami , Florida. 22-24 March 2013. sessions with peer reviewed paper presentations, Developments in the theory, application and with discussants and question and answer ope- practice of mathematical Finance/Financial En- ned to the ﬂoor. There will also be presentations gineering/Computational and Quantitative Fi- by invited speakers and panel discussion which nance continue at a rapid pace. This conference will also be opened to the ﬂoor. Working sessions

Content 20 www.bayesian.org ISBA Bulletin, 19(4), December 2012 NEWS FROM THE WORLD may be arranged. Additional information can be Bayesian Modeling for Cognitive Science, A found at http://www.bradley.edu/academic/ WinBUGS Workshop, University of Amsterdam continue/professionals/imfc/index.dot. on August 12-16, 2013.

9th Conference on Bayesian Nonparametrics, This workshop is meant for researchers who Amsterdam, Holland. 10 - 14 June, 2013. want to learn how to apply Bayesian inference in practice. Most applications we discuss are taken The Bayesian nonparametrics (BNP) conference from the field of cognitive science. Because the is a bi-annual international meeting bringing to- workshop is based on a set of book chapters and gether leading experts and talented young rese- concrete exercises of varying difficulty, the cour- archers working on applications and theory of se material is appropriate for researchers with nonparametric Bayesian statistics. It is an official a wide range of prior knowledge and interests. section meeting of the Bayesian nonparametrics Although some basic knowledge of Bayesian in- section of the International Society for Bayesian ference is an advantage, this is not a prerequisite. Analysis (ISBA) and is co-sponsored by the Insti- In the course we use WinBUGS in combination tute of Mathematical Statistics (IMS). with R or Matlab (the choice is yours), and there- Additional information can be found at http: fore somebasic knowledge of either R or Matlab //www.bnp9.win.tue.nl/. is also an advantage.

First Bayesian Young Statisticians Meeting, All information can be found on the confe- CNR IMATI in Milano on June 5-6, 2013. rence website at http://bayescourse.socsci. uva.nl. BAYSM 2013 is a fantastic opportunity to present and discuss your work with other young stati- 8th Workshop on Bayesian Inference in Stocha- sticians in a relaxed and friendly atmosphere, stic Processes (BISP8), CNR IMATI in Milano, with senior discussant giving you suggestions Italy, on June 6-8, 2013. and comments aimed at improving your work. The workshop is organised by CNR IMATI, in Attendees are encouraged to give a talk and/or cooperation with George Washington University, submit a poster. The meeting is aimed at ear- and it is endorsed by ISBA (International Society ly career statisticians, i.e. people carrying out a for Bayesian Analysis) and SIS (Italian Statisti- PhD, post-doc or ﬁnishing the Master Degree cal Society). Provisional programme and list of with outstanding theses/projects dealing with invited speakers are available. A guided tour of Bayesian statistics. Presentations on current PhD Pinacoteca di Brera, one of the most important research are therefore welcomed as well as talks art museums in Italy, is under planning, along on work in progress on applied experience. with a dinner in a typical restaurant. All information on BAYSM 2013, including the sign-up link for the conference and accommo- All information can be found on the confe- dation, can be found on the conference website rence website at http://www.mi.imati.cnr.it/ at http://www.mi.imati.cnr.it/conferences/ conferences/BISP8/. BAYSM2013/index.html. ▲

Content 21 www.bayesian.org ISBA Bulletin, 19(4), December 2012

Executive Committee Board Members:

President: Fabrizio Ruggeri 2012–2014: Past President: Michael I. Jordan Kate Calder, Maria de Iorio, Igor Prunster, Wess Johnson President Elect: Merlise Clyde Treasurer: Michael Daniels 2011–2013: Executive Secretary: Merlise Clyde Ming-Hui Chen, Chris Holmes, Antonietta Mira, Judith Rousseau Program Council 2010–2012: Siddhartha Chib, Arnaud Doucet, Peter Chair: Vanja Dukic Hoff, Raquel Prado Vice Chair: Raquel Prado Past Chair: Igor Pruenster

EDITORIAL BOARD

Editor

Manuel Mendoza [email protected]

Associate Editors

Software Highlight Students’ Corner Francisco Torres Isadora Antoniano & Antonio Ortiz [email protected] [email protected] [email protected]

Content 22 www.bayesian.org