## off to Luminy for a second Bayesian week

Posted in Statistics with tags , , , , , , , , , on November 23, 2018 by xi'an

## importance tempering and variable selection

Posted in Books, Statistics with tags , , , , , , , , on November 6, 2018 by xi'an

As reading and commenting the importance tempering for variable selection paper by Giacomo Zanella (previously Warwick) and Gareth Roberts (Warwick) has been on my to-do list for quite a while, the fact that Giacomo presented this work at CIRM Bayesian Masterclass last week was the right nudge to write this post.

The starting point for the method is to simulate from a tempered version of a Gibbs sampler, selecting the component [of the parameter vector θ] according to an importance weight that is the inverse of the conditional posterior to the complementary power. That is, the inverse of the importance weight. This approach differs from classical (MCMC) tempering in that it does not target the original distribution. Hence it produces a weighted sample, whose computing time is of the order of the dimension of θ, even though the tempered simulation of a single conditional can reduce the variance of the estimator. The method is generalisable to any collection of one-component proposal/importance distributions, with the assumption that they have fatter tails that the true conditionals. The resulting Markov chain is reversible with respect to another stationary measure made of the original distribution multiplied by the normalisation factor of the importance weights but this ensures that weighted averages converge to the right quantity. Interestingly so because the powered conditionals are not necessarily coherent from a Gibbsic perspective.

The method is applied to Bayesian [spike-and-slab] variable selection of variables, the importance selection of a subset of covariates being restricted to changing one index at a time. I did not understand first how the computation of the normalising constant avoids involving 2-to-the-power-p terms until Giacomo explained to me that the constant was only computed for conditionals. The complexity gets down from O(|γ|²) to O(|γ|p), where |γ| is the number of variables. Another question I had was about the tempering power β, which selection remains a wee bit of an art!

## Crêt Saint Michel

Posted in Mountains, pictures, Running, Travel with tags , , , , , , , , , on November 1, 2018 by xi'an

A great afternoon climbing near CIRM with Nicolas, a mountain guide from the local guide company in Cassis, on this cliff of Crêt Saint Michel I passed everyday [while there!] to go swimming in the Sormiou harbour below, a mere 15 mn run from CIRM. As shown by the above map of bolted routes on the first half of the cliff, there are plenty of choices and more, although there were already four other groups climbing on that afternoon.

All these routes are bolted and have been around for quite a while, meaning two significant things: the quotation of the difficulty of the routes is quite lax and the rock is weathered by use at places, which made going up a 5c route somewhat of a challenge for me when climbing second and an impossibility when climbing first. On the rightmost green route, the 6a+ part had bits where I had to rely on slings left by Nicolas.The weather was brilliant, with blue sky and hot sun all the way, and the view of the Sormiou calanque (creek) below as a terrific background… I hope I can repeat this experience when visiting CIRM again in November, for the “Big Bayes” conference. And even more that this unique coastline will not be reached by the growing oil spil in the area.

## trail to Sugiton [jatp]

Posted in Mountains, pictures, Running, Travel, University life with tags , , , , , , , , , , on October 26, 2018 by xi'an

## glorious dawn [jatp]

Posted in Mountains, pictures, Running, Travel, University life with tags , , , , , , , , , , , , , , , on October 25, 2018 by xi'an

## short course on MCMC at CiRM [slides]

Posted in Statistics with tags , , , , , , , , , , , , , , , on October 23, 2018 by xi'an

Here are the [recycled] slides for the introductory lecture I gave this morning at CIRM, with the side information that it appears Slideshare has gone to another of these stages when slides cannot be played on this blog [when using Firefox]…