Archive for Sormiou

off to Luminy!!!

Posted in Mountains, pictures, Running, Statistics, Travel, University life with tags , , , , , , , , , , , , on June 27, 2021 by xi'an

mare e monti [climbing up Rumpe Cuou]

Posted in Mountains, pictures, Running, Travel with tags , , , , , , , , , , , on December 18, 2018 by xi'an

While at CIRM for Bayes for Good and Big Bayes workshops, I went again climbing with Nicolas, a guide from Cassis. As we had picked a day when the mistral (a local Northeasterner) was high and made climbing unpleasant and freezing, Nicolas picked a domain on the `other’ side, that was completely protected and started from the sea and went up in the sun, the wind only hitting us at the top, after six pitches, most of which I managed to lead.

We proceeded fast enough to get down for a second route, just as pleasant, finishing at the top as the Sun was setting down behind the islands below us. A well-chosen set of levels (5b, 5c) and rock-types like slab for my level and a nice conslusion to three climbing outings within a month. (Note that most pictures of our route are not mine as my camera battery went down before we even started.)

a book by C.Robert [not a book review]

Posted in Books, Kids, pictures, Statistics, University life with tags , , , , , , , , , on December 10, 2018 by xi'an

sunset on Riou Island [jatp]

Posted in Mountains, pictures, Travel with tags , , , , , , , , , , , on November 30, 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!