Blog Archives

The answer is e, what was the question?!

February 11, 2016
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The answer is e, what was the question?!

A rather exotic question on X validated: since π can be approximated by random sampling over a unit square, is there an equivalent for approximating e? This is an interesting question, as, indeed, why not focus on e rather than π after all?! But very quickly the very artificiality of the problem comes back to

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optimal simulation on a convex set

February 3, 2016
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optimal simulation on a convex set

This morning, we had a jam session at the maths department of Paris-Dauphine where a few researchers & colleagues of mine presented their field of research to the whole department. Very interesting despite or thanks to the variety of topics, with forays into the three-body problem(s) , mean fields for Nash equilibrium (or

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Le Monde puzzle [#947]

February 1, 2016
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Le Monde puzzle [#947]

Another boardgame in Le Monde mathematical puzzle : Given an 8×8 chequerboard,  consider placing 2×2 tiles over this chequerboard until (a) the entire surface is covered and (b) removing a single 2×2 tile exposes some of the original chequerboard. What is the maximal number of 2×2 tiles one can set according to this scheme? And for

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love-hate Metropolis algorithm

January 27, 2016
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love-hate Metropolis algorithm

Hyungsuk Tak, Xiao-Li Meng and David van Dyk just arXived a paper on a multiple choice proposal in Metropolis-Hastings algorithms towards dealing with multimodal targets. Called “A repulsive-attractive Metropolis algorithm for multimodality” . The proposal distribution includes a downward

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R typos

January 26, 2016
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R typos

At MCMskv, Alexander Ly (from Amsterdam) pointed out to me some R programming mistakes I made in the introduction to Metropolis-Hastings algorithms I wrote a few months ago for the Wiley on-line encyclopedia! While the outcome (Monte Carlo posterior) of the corrected version is moderately changed this is nonetheless embarrassing! The example (if not the

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high dimension Metropolis-Hastings algorithms

January 25, 2016
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high dimension Metropolis-Hastings algorithms

When discussing high dimension models with Ingmar Schüster Schuster the other day, we came across the following paradox with Metropolis-Hastings algorithms. If attempting to simulate from a multivariate standard normal distribution in a large dimension, when starting from the mode of the target, i.e., its mean γ, leaving the

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MCqMC 2016

January 18, 2016
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MCqMC 2016

After the MCqMC 2014 conference in Leuven I enjoyed very much, the MCqMC 2016 instalment takes place in Stanford this (late) summer. I cannot alas attend it, as I will be in Australia all summer winter, but the program looks terrific! As Art’s tutorial so brilliantly showed at MCMskv last week, the connections between the

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precision in MCMC

January 13, 2016
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precision in MCMC

While browsing Images des Mathématiques, I came across this article that studies the impact of round-off errors on number representations in a dynamical system and checked how much this was the case for MCMC algorithms like the slice sampler (recycling some R code from Monte Carlo Statistical Methods). By simply adding a few

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MCMskv #5 [future with a view]

January 11, 2016
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MCMskv #5 [future with a view]

As I am flying back to Paris (with an afternoon committee meeting in München in-between), I am reminiscing on the superlative scientific quality of this MCMski meeting, on the novel directions in computational Bayesian statistics exhibited therein, and on the potential settings for the next meeting. If any. First, as hopefully obvious from my previous

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mixtures are slices of an orange

January 11, 2016
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mixtures are slices of an orange

After presenting this work in both London and Lenzerheide, Kaniav Kamary, Kate Lee and I arXived and submitted our paper on a new parametrisation of location-scale mixtures. Although it took a long while to finalise the paper, given that we came with the original and central idea about a year ago, I remain quite excited

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