Adrian Smith to head British replacement of ERC

Just read in Nature today that Adrian Smith (of MCMC fame!) was to head the search for a replacement to ERC and Marie Curie research funding in the UK. Adrian, whom I first met in Sherbrooke, Québec, in June 1989, when he delivered one of his first talks on MCMC, is currently the director of the Alan Turing Institute in London, of which Warwick is a constituent. (Just for the record, Chris Skimore is the current Science minister in Theresa May’s government and here is what he states and maybe even think about her Brexit deal: “It’s fantastic for science, it’s fantastic for universities, it’s fantastic for collaboration”) I am actually surprised at the notion of building a local alternative to the ERC when the ERC includes many countries outside the European Union and even outside Europe…

recycling Gibbs auxiliaries

Luca Martino, Victor Elvira and Gustau Camps-Valls have arXived a paper on recycling for Gibbs sampling. The argument therein is to take advantage of all simulations induced by MCMC simulation for one full conditional, towards improving estimation if not convergence. The context is thus one when Metropolis-within-Gibbs operates, with several (M) iterations of the corresponding Metropolis being run instead of only one (which is still valid from a theoretical perspective). While there are arguments in augmenting those iterations, as recalled in the paper, I am not a big fan of running a fixed number of M of iterations as this does not approximate better the simulation from the exact full conditional and even if this approximation was perfect, the goal remains simulating from the joint distribution. As such, multiplying the number of Metropolis iterations does not necessarily impact the convergence rate, only brings it closer to the standard Gibbs rate. Moreover, the improvement does varies with the chosen component, meaning that the different full conditionals have different characteristics that produce various levels of variance reduction:

• if the targeted expectation only depends on one component of the Markov chain, multiplying the number of simulations for the other components has no clear impact, except in increasing time;
• if the corresponding full conditional is very concentrated, repeating simulations should produce quasi-repetitions, and no gain.

The only advantage in computing time that I can see at this stage is when constructing the MCMC sampler for the full proposal is much more costly than repeating MCMC iterations, which are then almost free and contribute to the reduction of the variance of the estimator.

This analysis of MCMC-withing-Gibbs strategies reminds me of a recent X validated question, which was about the proper degree of splitting simulations from a marginal and from a corresponding conditional in the chain rule, the optimal balance being in my opinion dependent on the relative variances of the conditional expectations.

A last point is that recycling in the context of simulation and Monte Carlo methodology makes me immediately think of Rao-Blackwellisation, which is surprisingly absent from the current paper. Rao-Blackwellisation was introduced in the MCMC literature and to the MCMC community in the first papers of Alan Gelfand and Adrian Smith, in 1990. While this is not always producing a major gain in Monte Carlo variability, it remains a generic way of recycling auxiliary variables as shown, e.g., in the recycling paper we wrote with George Casella in 1996, one of my favourite papers.

the last digit of e

Éric Marchand from Sherbrooke, Québec [historical birthplace of MCMC, since Adrian Smith gave his first talk on his Gibbs sampler there, in June 1989], noticed my recent posts about the approximation of e by Monte Carlo methods and sent me a paper he wrote in The Mathematical Gazette of November 1995 [full MCMC era!] about original proofs on the expectation of some stopping rules being e, like the length of increasing runs. And Gnedenko’s uniform summation until exceeding one. Amazing that this simple problem generated so much investigation!!!

big Bayes stories

(The following is our preface to the incoming “Big Bayes stories” special issue of Statistical Science, edited by Sharon McGrayne, Kerrie Mengersen and myself.)

Bayesian statistics is now endemic in many areas of scientic, business and social research. Founded a quarter of a millenium ago, the enabling theory, models and computational tools have expanded exponentially in the past thirty years. So what is it that makes this approach so popular in practice? Now that Bayesian statistics has “grown up”, what has it got to show for it- self? In particular, what real-life problems has it really solved? A number of events motivated us to ask these questions: a conference in honour of Adrian Smith, one of the founders of modern Bayesian Statistics, which showcased a range of research emanating from his seminal work in the field, and the impressive book by Sharon McGrayne, the theory that would not die. At a café in Paris in 2011, we conceived the idea of gathering a similar collection of “Big Bayes stories”, that would demonstrate the appeal of adopting a Bayesian modelling approach in practice. That is, we wanted to collect real cases in which a Bayesian approach had made a significant difference, either in addressing problems that could not be analysed otherwise, or in generating a new or deeper understanding of the data and the associated real-life problem.

After submitting this proposal to Jon Wellner, editor of Statistical Science, and obtaining his encouragement and support, we made a call for proposals. We received around 30 submissions (for which authors are to be warmly thanked!) and after a regular review process by both Bayesian and non-Bayesian referees (who are also deeply thanked), we ended up with 17 papers that reflected the type of stories we had hoped to hear. Sharon McGrayne, then read each paper with the utmost attention and provided helpful and encouraging comments on all. Sharon became part the editorial team in acknowledgement of this substantial editing contribution, which has made the stories much more enjoyable. In addition, referees who handled several submissions were asked to contribute discussions about the stories and some of them managed to find additional time for this task, providing yet another perspective on the stories..

Bayesian Estimation of Population – Level Trends in Measures of Health Status	Mariel M. Finucane, Christopher J. Paciorek, Goodarz Danaei, and Majid Ezzati
Galaxy Formation: Bayesian History Matching for the Observable Universe	Ian Vernon, Michael Goldstein, and Richard G Bower
Estimating the Distribution of Dietary Consumption Patterns	Raymond James Carroll
Bayesian Population Projections for the United Nations	Adrian E. Raftery, Leontine Alkema, and Patrick Gerland
From Science to Management: Using Bayesian Networks to Learn about Lyngbya	Sandra Johnson, Eva Abal, Kathleen Ahern, and Grant Hamilton
Search for the Wreckage of Air France Flight AF 447	Lawrence D Stone, Colleen M. Keller, Thomas M Kratzke, and Johan P Strumpfer
Finding the most distant quasars using Bayesian selection methods	Daniel Mortlock
Estimation of HIV burden through Bayesian evidence synthesis	Daniela De Angelis, Anne M Presanis, Stefano Conti, and A E Ades
Experiences in Bayesian Inference in Baltic Salmon Management	Sakari Kuikka, Jarno Vanhatalo, Henni Pulkkinen, Samu Mäntyniemi, and Jukka Corander

As can be gathered from the table of contents, the spectrum of applications ranges across astronomy, epidemiology, ecology and demography, with the special case of the Air France wreckage story also reported in the paper- back edition of the theory that would not die. What made those cases so well suited for a Bayesian solution? In some situations, the prior or the expert opinion was crucial; in others, the complexity of the data model called for a hierarchical decomposition naturally provided in a Bayesian framework; and others involved many actors, perspectives and data sources that only Bayesian networks could aggregate. Now, before or (better) after reading those stories, one may wonder whether or not the “plus” brought by the Bayesian paradigm was truly significant. We think they did, at one level or another of the statistical analysis, while we acknowledge that in several cases other statistical perspectives or even other disciplines could have brought another solution, but presumably at a higher cost.

Now, before or (better) after reading those stories, one may wonder whether or not the \plus” brought by the Bayesian paradigm was truly significant. We think it did, at one level or another of the statistical analysis, while we acknowledge that in several cases other statistical perspectives or even other disciplines could have provided another solution, but presumably at a higher cost. We think this collection of papers constitutes a worthy tribute to the maturity of the Bayesian paradigm, appropriate for commemorating the 250th anniversary of the publication of Bayes’ Essay towards solving a Problem in the Doctrine of Chances. We thus hope you will enjoy those stories, whether or not Bayesiana is your statistical republic.

reading classics (#3)

Following in the reading classics series, my Master students in the Reading Classics Seminar course, listened today to Kaniav Kamary analysis of Denis Lindley’s and Adrian Smith’s 1972 linear Bayes paper Bayes Estimates for the Linear Model in JRSS Series B. Here are her (Beamer) slides

At a first (mathematical) level this is an easier paper in the list, because it relies on linear algebra and normal conditioning. Of course, this is not the reason why Bayes Estimates for the Linear Model is in the list and how it impacted the field. It is indeed one of the first expositions on hierarchical Bayes programming, with some bits of empirical Bayes shortcuts when computation got a wee in the way. (Remember, this is 1972, when shrinkage estimation and its empirical Bayes motivations is in full blast…and—despite Hstings’ 1970 Biometrika paper—MCMC is yet to be imagined, except maybe by Julian Besag!) So, at secondary and tertiary levels, it is again hard to discuss, esp. with Kaniav’s low fluency in English. For instance, a major concept in the paper is exchangeability, not such a surprise given Adrian Smith’s translation of de Finetti into English. But this is a hard concept if only looking at the algebra within the paper, as a motivation for exchangeability and partial exchangeability (and hierarchical models) comes from applied fields like animal breeding (as in Sørensen and Gianola’s book). Otherwise, piling normal priors on top of normal priors is lost on the students. An objection from a 2012 reader is also that the assumption of exchangeability on the parameters of a regression model does not really make sense when the regressors are not normalised (this is linked to yesterday’s nefarious post!): I much prefer the presentation we make of the linear model in Chapter 3 of our Bayesian Core. Based on Arnold Zellner‘s g-prior. An interesting question from one student was whether or not this paper still had any relevance, other than historical. I was a bit at a loss on how to answer as, again, at a first level, the algebra was somehow natural and, at a statistical level, less informative priors could be used. However, the idea of grouping parameters together in partial exchangeability clusters remained quite appealing and bound to provide gains in precision….