I just updated my short review on Bayesian computational tools I first wrote in April for the Annual Review of Statistics and Its Applications. The coverage is quite restricted, as I took advantage of two phantom papers I had started a while ago, one with Jean-Michel Marin, on hierarchical Bayes methods and on ABC. (As stressed in the first version, the paper handles missing data, not as a topic, but as a fact!) The running example is the Laplace vs. Gauss model choice problem, first considered in our ABC model choice paper. The referee of the paper was asking for a broader perspective, which makes perfect sense (except that I did not have the time to get that broad). And mentioned a potential missing acknowledgement of priority as Olli’s thesis was using a simple (instead of double) exponential vs. Gauss as its running example. Once again, a plain 25 pages introduction to the topic, not aiming at anything new. The exercise made me ponder whether or not I wanted to engage into it in a near future, with a pessimistic outcome!
Archive for hierarchical Bayesian modelling
(My colleague Jean-Louis Fouley, now at I3M, Montpellier, kindly agreed to write a review on the BUGS book for CHANCE. Here is the review, en avant-première! Watch out, it is fairly long and exhaustive! References will be available in the published version. The additions of book covers with BUGS in the title and of the corresponding Amazon links are mine!)
If a book has ever been so much desired in the world of statistics, it is for sure this one. Many people have been expecting it for more than 20 years ever since the WinBUGS software has been in use. Therefore, the tens of thousands of users of WinBUGS are indebted to the leading team of the BUGS project (D Lunn, C Jackson, N Best, A Thomas and D Spiegelhalter) for having eventually succeeded in finalizing the writing of this book and for making sure that the long-held expectations are not dashed.
As well explained in the Preface, the BUGS project initiated at Cambridge was a very ambitious one and at the forefront of the MCMC movement that revolutionized the development of Bayesian statistics in the early 90’s after the pioneering publication of Gelfand and Smith on Gibbs sampling.
This book comes out after several textbooks have already been published in the area of computational Bayesian statistics using BUGS and/or R (Gelman and Hill, 2007; Marin and Robert, 2007; Ntzoufras, 2009; Congdon, 2003, 2005, 2006, 2010; Kéry, 2010; Kéry and Schaub, 2011 and others). It is neither a theoretical book on foundations of Bayesian statistics (e.g. Bernardo and Smith, 1994; Robert, 2001) nor an academic textbook on Bayesian inference (Gelman et al, 2004, Carlin and Louis, 2008). Instead, it reflects very well the aims and spirit of the BUGS project and is meant to be a manual “for anyone who would like to apply Bayesian methods to real-world problems”.
In spite of its appearance, the book is not elementary. On the contrary, it addresses most of the critical issues faced by statisticians who want to apply Bayesian statistics in a clever and autonomous manner. Although very dense, its typical fluid British style of exposition based on real examples and simple arguments helps the reader to digest without too much pain such ingredients as regression and hierarchical models, model checking and comparison and all kinds of more sophisticated modelling approaches (spatial, mixture, time series, non linear with differential equations, non parametric, etc…).
The book consists of twelve chapters and three appendices specifically devoted to BUGS (A: syntax; B: functions and C: distributions) which are very helpful for practitioners. The book is illustrated with numerous examples. The exercises are well presented and explained, and the corresponding code is made available on a web site. Read more »
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….
Jean-Michel Marin visited me in Paris last week and, besides taking part in Pierre’s PhD defence, we made enough progress to close two more chapters of the new edition of Bayesian Core (soon to be Bayesian Essentials with R!) This follows the good work session we had in Carnon where we also completed two chapters (although it was hard to convince anyone that renting a flat by the Mediterranean sea was at all connected with…work! While it was: the only breaks I took were my morning runs…). There just remains one single chapter to complete, now, the one on hierarchical Bayes models. By all means, I dearly want to see it done by November 1!!!
Next month, Kerrie Mengersen (QUT, Brisbane, Australia, and visiting us at CREST and Paris-Dauphine this coming May) will give a PhD course at CREST on the theme of applied Bayesian statistical modelling.
Here is her abstract:
Bayesian hierarchical models are now widely used in addressing a rich variety of real-world problems. In this course, we will examine some common models and the associated computational methods used to solve these problems, with a focus on environmental and health applications.
Two types of hierarchical models will be considered, namely mixture models and spatial models. Computational methods will cover Markov chain Monte Carlo, Variational Bayes and Approximate Bayesian Computation.
Participants will have the opportunity to implement these approaches using a number of datasets taken from real case studies, including the analysis of digital images from animals and satellites, and disease mapping for medicine and biosecurity.
The classes will take place at ENSAE, Paris, on May 3, 10 (14:00, Amphi 2), 14, and 21 (11:00, Room S8). (The course is open to everyone and free of charge, but registrations are requested, please contact Nadine Guedj.)