Archive for August, 2010

Hyper-g priors

Posted in Books, R, Statistics with tags , , , , , , on August 31, 2010 by xi'an

Earlier this month, Daniel Sabanés Bové and Leo Held posted a paper about g-priors on arXiv. While I glanced at it for a few minutes, I did not have the chance to get a proper look at it till last Sunday. The g-prior was first introduced by the late Arnold Zellner for (standard) linear models, but they can be extended to generalised linear models (formalised by the late John Nelder) at little cost. In Bayesian Core, Jean-Michel Marin and I do centre the prior modelling in both linear and generalised linear models around g-priors, using the naïve extension for generalised linear models,

\beta \sim \mathcal{N}(0,g \sigma^2 (\mathbf{X}^\text{T}\mathbf{X})^{-1})

as in the linear case. Indeed, the reasonable alternative would be to include the true information matrix but since it depends on the parameter \beta outside the normal case this is not truly an alternative. Bové and Held propose a slightly different version

\beta \sim \mathcal{N}(0,g \sigma^2 c (\mathbf{X}^\text{T}\mathbf{W}\mathbf{X})^{-1})

where W is a diagonal weight matrix and c is a family dependent scale factor evaluated at the mode 0. As in Liang et al. (2008, JASA) and most of the current literature, they also separate the intercept \beta_0 from the other regression coefficients. They also burn their “improperness joker” by choosing a flat prior on \beta_0, which means they need to use a proper prior on g, again as Liang et al. (2008, JASA), for the corresponding Bayesian model comparison to be valid. In Bayesian Core, we do not separate \beta_0 from the other regression coefficients and hence are left with one degree of freedom that we spend in choosing an improper prior on g instead. (Hence I do not get the remark of Bové and Held that our choice “prohibits Bayes factor comparisons with the null model“. As argued in Bayesian Core, the factor g being an hyperparameter shared by all models, we can use the same improper prior on g in all models and hence use standard Bayes factors.) In order to achieve closed form expressions, the authors use Cui and George ‘s (2008) prior

\pi(g) \propto (1+g)^{1+a}\exp\{-b/(1+g)\}

which requires the two hyper-hyper-parameters a and b to be specified.

The second part of the paper considers computational issues. It compares the ILA solution of Rue, Martino and Chopin (2009, Series B) with an MCMC solution based on an independent proposal on g resulting from linear interpolations (?). The marginal likelihoods are approximated by Chib and Jeliazkov (2001, JASA) for the MCMC part. Unsurprisingly, ILA does much better, even with a 97% acceptance rate in the MCMC algorithm.

The paper is very well-written and quite informative about the existing literature. It also uses the Pima Indian dataset  (The authors even dug out a 1991 paper of mine I had completely forgotten!) I am actually thinking of using the review in our revision of Bayesian Core, even though I think we should stick to our choice of including \beta_0 within the set of parameters…

Beta translation done!

Posted in Books, R, Statistics, University life with tags , , , , on August 30, 2010 by xi'an

Introducting Monte CarloOnce my team of four translators had handed back to me all the chapters of the French version of Introducing Monte Carlo Methods with R to me, I had to go over the book to ensure some minimal consistency between the chapters. I started the editing in the plane to Vancouver but did not get much done until last Monday when arriving in Long Beach. After three days of hard work, here at home, I am now done with the beta version of the translation and I have sent it to the French Springer editor… I hope he will not ask for deep changes as I have absolutely no time left in my schedule for the coming months!

Incoherent phylogeographic inference [accepted]

Posted in Statistics, University life with tags , , , , , on August 30, 2010 by xi'an

The letter we submitted to PNAS about Templeton’s surprising diatribe on Bayesian inference has now been accepted:

Title: “Incoherent Phylogeographic Inference”
Tracking #: 2010-08762
Authors: Berger et al.

Dear Prof. Robert,
We are pleased to inform you that the PNAS Editorial Board has given final approval of your letter to the Editor for online publication. The author(s) of the published manuscript have been invited to respond to your feedback. If they provide a response, it may appear online concurrently with your letter.

Now we are looking forward (?) Alan Templeton’s answer, even though I suspect this short letter is not going to have any impact on his views!

Dexter on stage

Posted in Kids, Travel with tags , , , on August 29, 2010 by xi'an

Staying “near” Hollywood (in Long Beach) has some unpredictable rewards: we had the pleasant surprise on the last and final day of our vacations to see a filming crew invade the street where we were staying and setting up the stage for filming an accident scene of the [gory] TV-show Dexter, which is a favourite of my son’s. The crew arrived fairly early while I was out running and we had been warned the day before to move our car to a back street. My kids had a great morning watching the preparation of the street, 20m from our house, and then the various filming stages, culminating with the arrival of Michael C. Hall who is playing Dexter (and who waived at them when parking in from of our rental place, presumably making those last hours the most memorable ones of their vacations, while Yosemite was undoubtedly the lowest time!). Here are a few pictures they took during the whole occurence. (The trucks appearing in the show  all mention Miami as this is where the action is taking place.)

While I did not watch the process for very long, catching the opportunity to work peacefully on the translation, I was rather surprised by the static nature of the game. The two cars involved in the accident were brought on a truck, the crash most likely taking place in a studio, and the aftermath of the accident did not seem to fill that much time in the show, despite requiring a full day of work…

Dead trees of the upper Yosemite

Posted in Mountains, pictures, Travel with tags , on August 28, 2010 by xi'an

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