## Archive for Purdue University

## patterned random matrices [not a book review]

Posted in Books, pictures, Statistics, University life with tags Arup Bose, book review, Indian Statistical Institute, Kolkata, Purdue University, random matrices on October 24, 2018 by xi'an## a jump back in time

Posted in Books, Kids, Statistics, Travel, University life with tags Bayesian statistics, Fortran, French army, LaTeX, mixture of distributions, noninformative priors, Purdue University, S, software, Spain, Valencia 3, Valencia conferences on October 1, 2018 by xi'an**A**s the Department of Statistics in Warwick is slowly emptying its shelves and offices for the big migration to the new building that is almost completed, books and documents are abandoned in the corridors and the work spaces. On this occasion, I thus happened to spot a vintage edition of the Valencia 3 proceedings. I had missed this meeting and hence the volume for, during the last year of my PhD, I was drafted in the French Navy and as a result prohibited to travel abroad. (Although on reflection I could have safely done it with no one in the military the wiser!) Reading through the papers thirty years later is a weird experience, as I do not remember most of the papers, the exception being the mixture modelling paper by José Bernardo and Javier Giròn which I studied a few years later when writing the mixture estimation and simulation paper with Jean Diebolt. And then again in our much more recent non-informative paper with Clara Grazian. And Prem Goel’s survey of Bayesian software. That is, 1987 state of the art software. Covering an amazing eighteen list. Including versions by Zellner, Tierney, Schervish, Smith [but no MCMC], Jaynes, Goldstein, Geweke, van Dijk, Bauwens, which apparently did not survive the ages till now. Most were in Fortran but S was also mentioned. And another version of Tierney, Kass and Kadane on Laplace approximations. And the reference paper of Dennis Lindley [who was already retired from UCL at that time!] on the Hardy-Weinberg equilibrium. And another paper by Don Rubin on using SIR (Rubin, 1983) for simulating from posterior distributions with missing data. Ten years before the particle filter paper, and apparently missing the possibility of weights with infinite variance.

There already were some illustrations of Bayesian analysis in action, including one by Jay Kadane reproduced in his book. And several papers by Jim Berger, Tony O’Hagan, Luis Pericchi and others on imprecise Bayesian modelling, which was in tune with the era, the imprecise probability book by Peter Walley about to appear. And a paper by Shaw on numerical integration that mentioned quasi-random methods. Applied to a 12 component Normal mixture.Overall, a much less theoretical content than I would have expected. And nothing about shrinkage estimators, although a fraction of the speakers had worked on this topic most recently.

At a less fundamental level, this was a time when ~~La~~TeX was becoming a standard, as shown by a few papers in the volume (and as I was to find when visiting Purdue the year after), even though most were still typed on a typewriter, including a manuscript addition by Dennis Lindley. And Warwick appeared as a Bayesian hotpot!, with at least five papers written by people there permanently or on a long term visit. (In case a local is interested in it, I have kept the volume, to be found in my new office!)

## divide & reconquer

Posted in Books, Statistics, University life with tags arXiv, contour, contour algorithm, divide-and-conquer strategy, harmonic mean estimator, HPD region, large data problems, nested sampling, Purdue University, skewed distribution, sub-likelihood on February 5, 2018 by xi'an**Q**i Liu, Anindya Bhadra, and William Cleveland from Purdue have arXived a paper entitled *Divide and Recombine for Large and Complex Data: Model Likelihood Functions using MCMC*. Which is a variation on the earlier divide & … papers attempting at handling large datasets. The beginning is quite similar to these earlier papers in that the likelihood is split into sub-likelihoods, approximated from MCMC samples and recombined into an approximate full likelihood. As in for instance Scott et al. one approximation use for the subsample is to replace the likelihood with a Normal approximation, or a skew Normal generalisation, which remains a limited choice for heavy tailed likelihoods. Producing a Normal and skew-Normal approximation for the whole [data] likelihood, respectively. If I understand correctly, these approximations are missing a normalising constant to bring them to scale with the true likelihood, which I do not completely understand as the likelihood only needs to be defined up to a [constant] constant for most purposes, including Bayesian ones. The method of estimation of this constant proposed therein is called the *contour probability algorithm* and it consists in using a highest density region to compare a likelihood and its approximation. (Nothing to do with our adaptation of Gelfand and Dey (1994) based on HPDs, with Darren Wright. Nor with nested sampling.) Returning a form of qq-plot. This is rather exploratory, while hardly addressing the issue of the precision of such approximations and the resolution of conflicting proposals. And the comparison with all these other recent proposals for splitting likelihoods into manageable bits (proposals that are mentioned in the final section, including our recentering scheme with my student Changye Wu).

## Jayanta Kumar Ghosh [1937-2017]

Posted in Books, pictures, Statistics, Travel, University life with tags An Introduction to Bayesian Statistics, Bayesians, higher order asymptotics, Indian Statistical Institute, ISI, J.K. Ghosh, Kolkata, Purdue University, West Lafayette on October 2, 2017 by xi'an**J**ust head from Sonia and Judith that our friend and fellow Bayesian Jayanta K Ghosh (জয়ন্ত কুমার ঘোষ in Bengali) has passed away a few days ago in Lafayette. He was a wonderful man, very kind to everyone and open for discussing all aspects of Bayesian theory and methodology. While he worked on many branches of statistics, he is more know to Bayesians for his contributions to Bayesian asymptotics. From Bernstein-von-Mises convergence theorems to frequentist validation of non-informative priors, to the Bayesian analysis of infinite dimensional problems, including consistency of posteriors and rates of convergence, and to Bayesian and Empirical Bayes model selection rules in high dimensional problems. He also wrote an introductory textbook on Bayesian Statistics ten years ago with Mohan Delampady and Tapas Samanta. And a monograph of higher order asymptotics. I knew from this summer that J K was quite sick and am quite sad to learn of his demise. He will be missed by all for his gentleness and by Bayesians for his contributions to the fields of objective and non-parametric Bayesian statistics…

## Robert’s paradox [reading in Reading]

Posted in Statistics, Travel, University life with tags BayesComp, biking, Chib's approximation, doubly intractable problems, exchange algorithm, exchangeability, John Deely, label switching, mixture estimation, Purdue University, trains, University of Oxford, University of Reading on January 28, 2015 by xi'an**O**n Wednesday afternoon, Richard Everitt and Dennis Prangle organised an RSS workshop in Reading on Bayesian Computation. And invited me to give a talk there, along with John Hemmings, Christophe Andrieu, Marcelo Pereyra, and themselves. Given the proximity between Oxford and Reading, this felt like a neighbourly visit, especially when I realised I could take my bike on the train! John Hemmings gave a presentation on synthetic models for climate change and their evaluation, which could have some connection with Tony O’Hagan’s recent talk in Warwick, Dennis told us about “the lazier ABC” version in connection with his “lazy ABC” paper, [from my very personal view] Marcelo expanded on the Moreau-Yoshida expansion he had presented in Bristol about six months ago, with the notion that using a Gaussian tail regularisation of a super-Gaussian target in a Langevin algorithm could produce better convergence guarantees than the competition, including Hamiltonian Monte Carlo, Luke Kelly spoke about an extension of phylogenetic trees using a notion of lateral transfer, and Richard introduced a notion of biased approximation to Metropolis-Hasting acceptance ratios, notion that I found quite attractive if not completely formalised, as there should be a Monte Carlo equivalent to the improvement brought by biased Bayes estimators over unbiased classical counterparts. (Repeating a remark by Persi Diaconis made more than 20 years ago.) Christophe Andrieu also exposed some recent developments of his on exact approximations à la Andrieu and Roberts (2009).

Since those developments are not yet finalised into an archived document, I will not delve into the details, but I found the results quite impressive and worth exploring, so I am looking forward to the incoming publication. One aspect of the talk which I can comment on is related to the exchange algorithm of Murray et al. (2006). Let me recall that this algorithm handles double intractable problems (i.e., likelihoods with intractable normalising constants like the Ising model), by introducing auxiliary variables with the same distribution as the data given the new value of the parameter and computing an augmented acceptance ratio which expectation is the targeted acceptance ratio and which conveniently removes the unknown normalising constants. This auxiliary scheme produces a random acceptance ratio and hence differs from the exact-approximation MCMC approach, which target directly the intractable likelihood. It somewhat replaces the unknown constant with the density taken at a plausible realisation, hence providing a proper scale. At least for the new value. I wonder if a comparison has been conducted between both versions, the naïve intuition being that the ratio of estimates should be more variable than the estimate of the ratio. More generally, it seemed to me [during the introductory part of Christophe’s talk] that those different methods always faced a harmonic mean danger when being phrased as expectations of ratios, since those ratios were not necessarily squared integrable. And not necessarily bounded. Hence my rather gratuitous suggestion of using other tools than the expectation, like maybe a median, thus circling back to the biased estimators of Richard. (And later cycling back, unscathed, to Reading station!)

On top of the six talks in the afternoon, there was a small poster session during the tea break, where I met Garth Holloway, working in agricultural economics, who happened to be a (unsuspected) fan of mine!, to the point of entitling his poster “Robert’s paradox”!!! The problem covered by this undeserved denomination connected to the bias in Chib’s approximation of the evidence in mixture estimation, a phenomenon that I related to the exchangeability of the component parameters in an earlier paper or set of slides. So “my” paradox is essentially label (un)switching and its consequences. For which I cannot claim any fame! Still, I am looking forward the completed version of this poster to discuss Garth’s solution, but we had a beer together after the talks, drinking to the health of our mutual friend John Deely.

## hasta luego, Susie!

Posted in Statistics, University life with tags Bayesian foundations, Cornell University, George Casella, ISBA, O'Bayes, Purdue University, Spain, Susie Bayarri, València on August 20, 2014 by xi'an**I** just heard that our dear, dear friend Susie Bayarri passed away early this morning, on August 19, in Valencià, Spain… I had known Susie for many, many years, our first meeting being in Purdue in 1987, and we shared many, many great times during simultaneous visits to Purdue University and Cornell University in the 1990’s. During a workshop in Cornell organised by George Casella (to become the unforgettable Camp Casella!), we shared a flat together and our common breakfasts led her to make fun of my abnormal consumption of cereals forever after, a recurrent joke each time we met! Another time, we were coming from the movie theatre in Lafayette in Susie’ s car when we got stopped for going through a red light. Although she tried very hard, her humour and Spanish verve were for once insufficient to convince her interlocutor.

**S**usie was a great Bayesian, contributing to the foundations of Bayesian testing in her numerous papers and through the direction of deep PhD theses in Valencia. As well as to queuing systems and computer models. She was also incredibly active in ISBA, from the very start of the Bayesian society, and was one of the first ISBA presidents. She also definitely contributed to the Objective Bayes section of ISBA, especially in the construction of the O’Bayes meetings. She gave a great tutorial on Bayes factors at the last O’Bayes conference in Duke last December, full of jokes and passion, despite being already weak from her cancer…

So, hasta luego, Susie!, from all your friends. I know we shared the same attitude about our Catholic education and our first names heavily laden with religious meaning, but I’d still like to believe that your rich and contagious laugh now resonates throughout the cosmos. So, hasta luego, Susie, and un abrazo to all of us missing her.

## marathon de Toulouse

Posted in Running with tags 5K, Indiana, marathon, Purdue University, road races, Toulouse, West Lafayette on October 27, 2013 by xi'an**C**ongratulations to Jean-Michel Marin, running his very first marathon in Toulouse this morning! I presume this is in part due to my bad influence, just like George Casella started me running road races (with the World famous Happy Hollow 5K in West Lafayette!)…