Archive for Series B

Conditional love [guest post]

Posted in Books, Kids, Statistics, University life with tags , , , , , , , , , , , , , , , , , , , , on August 4, 2015 by xi'an

[When Dan Simpson told me he was reading Terenin’s and Draper’s latest arXival in a nice Bath pub—and not a nice bath tub!—, I asked him for a blog entry and he agreed. Here is his piece, read at your own risk! If you remember to skip the part about Céline Dion, you should enjoy it very much!!!]

Probability has traditionally been described, as per Kolmogorov and his ardent follower Katy Perry, unconditionally. This is, of course, excellent for those of us who really like measure theory, as the maths is identical. Unfortunately mathematical convenience is not necessarily enough and a large part of the applied statistical community is working with Bayesian methods. These are unavoidably conditional and, as such, it is natural to ask if there is a fundamentally conditional basis for probability.

Bruno de Finetti—and later Richard Cox and Edwin Jaynes—considered conditional bases for Bayesian probability that are, unfortunately, incomplete. The critical problem is that they mainly consider finite state spaces and construct finitely additive systems of conditional probability. For a variety of reasons, neither of these restrictions hold much truck in the modern world of statistics.

In a recently arXiv’d paper, Alexander Terenin and David Draper devise a set of axioms that make the Cox-Jaynes system of conditional probability rigorous. Furthermore, they show that the complete set of Kolmogorov axioms (including countable additivity) can be derived as theorems from their axioms by conditioning on the entire sample space.

This is a deep and fundamental paper, which unfortunately means that I most probably do not grasp it’s complexities (especially as, for some reason, I keep reading it in pubs!). However I’m going to have a shot at having some thoughts on it, because I feel like it’s the sort of paper one should have thoughts on. Continue reading

discussions on Gerber and Chopin

Posted in Books, Kids, Statistics, University life with tags , , , , , , , , , , , , , , , on May 29, 2015 by xi'an

As a coincidence, I received my copy of JRSS Series B with the Read Paper by Mathieu Gerber and Nicolas Chopin on sequential quasi Monte Carlo just as I was preparing an arXival of a few discussions on the paper! Among the [numerous and diverse] discussions, a few were of particular interest to me [I highlighted members of the University of Warwick and of Université Paris-Dauphine to suggest potential biases!]:

  1. Mike Pitt (Warwick), Murray Pollock et al.  (Warwick) and Finke et al. (Warwick) all suggested combining quasi Monte Carlo with pseudomarginal Metropolis-Hastings, pMCMC (Pitt) and Rao-Bklackwellisation (Finke et al.);
  2. Arnaud Doucet pointed out that John Skilling had used the Hilbert (ordering) curve in a 2004 paper;
  3. Chris Oates, Dan Simpson and Mark Girolami (Warwick) suggested combining quasi Monte Carlo with their functional control variate idea;
  4. Richard Everitt wondered about the dimension barrier of d=6 and about possible slice extensions;
  5. Zhijian He and Art Owen pointed out simple solutions to handle a random number of uniforms (for simulating each step in sequential Monte Carlo), namely to start with quasi Monte Carlo and end up with regular Monte Carlo, in an hybrid manner;
  6. Hans Künsch points out the connection with systematic resampling à la Carpenter, Clifford and Fearnhead (1999) and wonders about separating the impact of quasi Monte Carlo between resampling and propagating [which vaguely links to one of my comments];
  7. Pierre L’Ecuyer points out a possible improvement over the Hilbert curve by a preliminary sorting;
  8. Frederik Lindsten and Sumeet Singh propose using ABC to extend the backward smoother to intractable cases [but still with a fixed number of uniforms to use at each step], as well as Mateu and Ryder (Paris-Dauphine) for a more general class of intractable models;
  9. Omiros Papaspiliopoulos wonders at the possibility of a quasi Markov chain with “low discrepancy paths”;
  10. Daniel Rudolf suggest linking the error rate of sequential quasi Monte Carlo with the bounds of Vapnik and Ĉervonenkis (1977).

 The arXiv document also includes the discussions by Julyan Arbel and Igor Prünster (Turino) on the Bayesian nonparametric side of sqMC and by Robin Ryder (Dauphine) on the potential of sqMC for ABC.

Relevant statistics for Bayesian model choice [hot off the press!]

Posted in Books, Statistics, University life with tags , , , , , , on October 30, 2014 by xi'an

jrssbabcOur paper about evaluating statistics used for ABC model choice has just appeared in Series B! It somewhat paradoxical that it comes out just a few days after we submitted our paper on using random forests for Bayesian model choice, thus bypassing the need for selecting those summary statistics by incorporating all statistics available and letting the trees automatically rank those statistics in term of their discriminating power. Nonetheless, this paper remains an exciting piece of work (!) as it addresses the more general and pressing question of the validity of running a Bayesian analysis with only part of the information contained in the data. Quite usefull in my (biased) opinion when considering the emergence of approximate inference already discussed on this ‘Og…

[As a trivial aside, I had first used fresh from the press(es) as the bracketted comment, before I realised the meaning was not necessarily the same in English and in French.]

Series B reaches 5.721 impact factor!

Posted in Books, Statistics, University life with tags , , , on September 15, 2014 by xi'an

I received this email from Wiley with the great figure that JRSS Series B has now reached a 5.721 impact factor. Which makes it the first journal in Statistics from this perspective. Congrats to editors Gareth Roberts, Piotr Fryzlewicz and Ingrid Van Keilegom for this achievement! An amazing jump from the 2009 figure of 2.84…!

this issue of Series B

Posted in Books, Statistics, Travel, University life with tags , , , , , , , , , , on September 5, 2014 by xi'an

The September issue of [JRSS] Series B I received a few days ago is of particular interest to me. (And not as an ex-co-editor since I was never involved in any of those papers!) To wit: a paper by Hani Doss and Aixin Tan on evaluating normalising constants based on MCMC output, a preliminary version I had seen at a previous JSM meeting, a paper by Nick Polson, James Scott and Jesse Windle on the Bayesian bridge, connected with Nick’s talk in Boston earlier this month, yet another paper by Ariel Kleiner, Ameet Talwalkar, Purnamrita Sarkar and Michael Jordan on the bag of little bootstraps, which presentation I heard Michael deliver a few times when he was in Paris. (Obviously, this does not imply any negative judgement on the other papers of this issue!)

For instance, Doss and Tan consider the multiple mixture estimator [my wording, the authors do not give the method a name, referring to Vardi (1985) but missing the connection with Owen and Zhou (2000)] of k ratios of normalising constants, namely

\sum_{l=1}^k \frac{1}{n_l} \sum_{t=1}^{n_l} \dfrac{n_l g_j(x_t^l)}{\sum_{s=1}^k n_s g_s(x_t^l) z_1/z_s } \longrightarrow \dfrac{z_j}{z_1}

where the z’s are the normalising constants and with possible different numbers of iterations of each Markov chain. An interesting starting point (that Hans Künsch had mentioned to me a while ago but that I had since then forgotten) is that the problem was reformulated by Charlie Geyer (1994) as a quasi-likelihood estimation where the ratios of all z’s relative to one reference density are the unknowns. This is doubling interesting, actually, because it restates the constant estimation problem into a statistical light and thus somewhat relates to the infamous “paradox” raised by Larry Wasserman a while ago. The novelty in the paper is (a) to derive an optimal estimator of the ratios of normalising constants in the Markov case, essentially accounting for possibly different lengths of the Markov chains, and (b) to estimate the variance matrix of the ratio estimate by regeneration arguments. A favourite tool of mine, at least theoretically as practically useful minorising conditions are hard to come by, if at all available.

Statistics and Computing special MCMSk’issue [call for papers]

Posted in Books, Mountains, R, Statistics, University life with tags , , , , , , , , , , , on February 7, 2014 by xi'an

moonriseFollowing the exciting and innovative talks, posters and discussions at MCMski IV, the editor of Statistics and Computing, Mark Girolami (who also happens to be the new president-elect of the BayesComp section of ISBA, which is taking over the management of future MCMski meetings), kindly proposed to publish a special issue of the journal open to all participants to the meeting. Not only to speakers, mind, but to all participants.

So if you are interested in submitting a paper to this special issue of a computational statistics journal that is very close to our MCMski themes, I encourage you to do so. (Especially if you missed the COLT 2014 deadline!) The deadline for submissions is set on March 15 (a wee bit tight but we would dearly like to publish the issue in 2014, namely the same year as the meeting.) Submissions are to be made through the Statistics and Computing portal, with a mention that they are intended for the special issue.

An editorial committee chaired by Antonietta Mira and composed of Christophe Andrieu, Brad Carlin, Nicolas Chopin, Jukka Corander, Colin Fox, Nial Friel, Chris Holmes, Gareth Jones, Peter Müller, Antonietta Mira, Geoff Nicholls, Gareth Roberts, Håvård Rue, Robin Ryder, and myself, will examine the submissions and get back within a few weeks to the authors. In a spirit similar to the JRSS Read Paper procedure, submissions will first be examined collectively, before being sent to referees. We plan to publish the reviews as well, in order to include a global set of comments on the accepted papers. We intend to do it in The Economist style, i.e. as a set of edited anonymous comments. Usual instructions for Statistics and Computing apply, with the additional requirements that the paper should be around 10 pages and include at least one author who took part in MCMski IV.

Series B news

Posted in Books, Statistics, University life with tags , , , , , , , , , , on January 24, 2014 by xi'an

IMG_2451IMG_2450The Journal of the Royal Statistical Society, Series B, has a new cover, a new colour and a new co-editor. As can be seen from the above shots, the colour is now a greenish ochre, with a picture of pedestrians on a brick plaza as a background, not much related to statistical methodology as far as I can tell. More importantly, the new co-editor for the coming four years is Piotr Fryzlewicz, professor at the London School of Economics, who will share the burden with Ingrid van Keilegom professor from UCL (Louvain-la-Neuve) who is now starting her third year… My friend, colleague and successor as Series B editor Gareth Roberts is now retiring after four years of hard work towards making Series B one of the top journals in Statistics. Thanks Gareth and best wishes to Ingrid and Piotr!

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