gives rises to as many auxiliary variables as there are components, minus one: namely, if a simulation * z* is generated from a given component

Filed under: Kids, Statistics, University life Tagged: Carlin, Gaussian mixture, mixtures ]]>

**F**or those interested in visiting Toulouse at the end of the summer for a French speaking conference in Probability and Statistics, the Modélisation-Aléatoire-Statistique branch of SMAI (the French version of SIAM) is holding its yearly conference. The main theme this year is “High dimension phenomena”, but a large panel of the French research in Probability and Statistics will be represented. The program contains in particular:

- Six plenary conferences and 3 talks by the recent winners of the “Prix Jacques Neveu” award [including Pierre Jacob!],
- 22 parallel sessions, from probability theory to applied statistics and machine learning,
- Posters session for students

More detail is available on the conference website (in French). (The organizing committee is made of Aurélien Garivier, Sébastien Gerchinovitz, Aldéric Joulin, Clément Pellegrini, and Laurent Risser.)

Filed under: Kids, pictures, Travel, University life, Wines Tagged: France, Jacques Neveu, MAS, MAS2014, Pierre Jacob, SMAI, Statistics conference, Toulouse ]]>

Filed under: pictures, Running, Statistics, Travel, University life, Wines Tagged: Berlin, Brussels, ISBA 2016, Leuven, MCMSki IV, MCQMC2014, train, WSC 2012 ]]>

*“At equilibrium, we thus should not expect gains of several orders of magnitude.”*

**A**s was signaled to me several times during the MCqMC conference in Leuven, Rémi Bardenet, Arnaud Doucet and Chris Holmes (all from Oxford) just wrote a short paper for the proceedings of ICML on a way to speed up Metropolis-Hastings by reducing the number of terms one computes in the likelihood ratio involved in the acceptance probability, i.e.

The observations appearing in this likelihood ratio are a random subsample from the original sample. Even though this leads to an unbiased estimator of the true log-likelihood sum, this approach is not justified on a pseudo-marginal basis à la Andrieu-Roberts (2009). (Writing this in the train back to Paris, I am not convinced this approach is in fact applicable to this proposal as the likelihood itself is not estimated in an unbiased manner…)

**I**n the paper, the quality of the approximation is evaluated by Hoeffding’s like inequalities, which serves as the basis for a stopping rule on the number of terms eventually evaluated in the random subsample. In fine, the method uses a sequential procedure to determine if enough terms are used to take the decision and the probability to take the same decision as with the whole sample is bounded from below. The sequential nature of the algorithm requires to either recompute the vector of likelihood terms for the previous value of the parameter or to store all of them for deriving the partial ratios. While the authors adress the issue of self-evaluating whether or not this complication is worth the effort, I wonder (from my train seat) why they focus so much on recovering the same decision as with the complete likelihood ratio and the same uniform. It would suffice to get the same distribution for the decision (an alternative that is easier to propose than to create of course). I also (idly) wonder if a Gibbs version would be manageable, i.e. by changing only some terms in the likelihood ratio at each iteration, in which case the method could be exact… (I found the above quote quite relevant as, in an alternative technique we are constructing with Marco Banterle, the speedup is particularly visible in the warmup stage.) Hence another direction in this recent flow of papers attempting to speed up MCMC methods against the incoming tsunami of “Big Data” problems.

Filed under: pictures, Statistics, Travel Tagged: acceptance rate, Brussels, Gibbs sampler, Hoeffding, ICML, Leuven, MCMC, MCQMC2014, Metropolis-Hastings algorithms, Paris, sequential Monte Carlo, speedup ]]>

Filed under: pictures, Running, Travel, University life Tagged: 17th Century house, Belgium, Grand Béguinage, Leuven, religious order ]]>

Filed under: pictures, Travel Tagged: Chile, forest fire, ISBA, ISBA 2004, Valparaiso ]]>

Filed under: Mountains, Running, Travel Tagged: amputation, anniversary, Banff, climbing accident, indoor climbing, prosthesis, thumb ]]>
**A**fter *Broken Blade* and its sequel *Bared Blade,* Kelly McCullough wrote *Crossed Blades* that I had ordered along with *Bared Blade*. And once again I read this volume within a few evenings. It is still very enjoyable, maybe the more given that there is a continuity in the characters and the plots. However, I did prefer *Bared Blade* to *Crossed Blades* as the former was creative in terms of plot and environment. Here, in *Crossed Blades*, the main character Aral is facing his past, from the destruction of his religious order and of his goddess to the possible treachery of former friends and mentors, to his attempt to drown this past in top quality whisky… While dealing with an adopted teenage daughter in the midst of a typical teenage crisis. This new instalment is thus full of introspection and reminiscence of past loves, and frankly a bit dull at times, even though there is a (spoiler warning!!) massive battle against the culprits for the destruction of the order. The very end is a bit disappointing, but it also hopefully closes a chapter in the hero’s life, which means that the next volume, *Blade Reforged*, may run into new territories and more into simili-detective stories. (Two more books in this Blade series are in the making!)

Filed under: Books Tagged: barren blade, blade reforged, book reviews, broken blade, crossed blades, heroic fantasy, Kelly McCullough, magics ]]>

Filed under: pictures, Running, Travel Tagged: Belgium, fog, Kasteel van Arenberg, Leuven, sunrise ]]>

Filed under: Books, Kids, R, University life Tagged: intToBits(), Le Monde, mathematical puzzle, R, StackExchange, stackoverflow ]]>