Archive for boulevard périphérique

Tractable Fully Bayesian inference via convex optimization and optimal transport theory

Posted in Books, Statistics, University life with tags , , , , , , , , on October 6, 2015 by xi'an

IMG_0294“Recently, El Moselhy et al. proposed a method to construct a map that pushed forward the prior measure to the posterior measure, casting Bayesian inference as an optimal transport problem. Namely, the constructed map transforms a random variable distributed according to the prior into another random variable distributed according to the posterior. This approach is conceptually different from previous methods, including sampling and approximation methods.”

Yesterday, Kim et al. arXived a paper with the above title, linking transport theory with Bayesian inference. Rather strangely, they motivate the transport theory with Galton’s quincunx, when the apparatus is a discrete version of the inverse cdf transform… Of course, in higher dimensions, there is no longer a straightforward transform and the paper shows (or recalls) that there exists a unique solution with positive Jacobian for log-concave posteriors. For instance, log-concave priors and likelihoods. This solution remains however a virtual notion in practice and an approximation is constructed via a (finite) functional polynomial basis. And minimising an empirical version of the Kullback-Leibler distance.

I am somewhat uncertain as to how and why apply such a transform to simulations from the prior (which thus has to be proper). Producing simulations from the posterior certainly is a traditional way to approximate Bayesian inference and this is thus one approach to this simulation. However, the discussion of the advantage of this approach over, say, MCMC, is quite limited. There is no comparison with alternative simulation or non-simulation methods and the computing time for the transport function derivation. And on the impact of the dimension of the parameter space on the computing time. In connection with recent discussions on probabilistic numerics and super-optimal convergence rates, Given that it relies on simulations, I doubt optimal transport can do better than O(√n) rates. One side remark about deriving posterior credible regions from (HPD)  prior credible regions: there is no reason the resulting region is optimal in volume (HPD) given that the transform is non-linear.

life and death along the RER B, minus approximations

Posted in Statistics, Travel with tags , , , , , , , , , , , , , , on June 30, 2015 by xi'an

viemortrerbWhile cooking for a late Sunday lunch today [sweet-potatoes röstis], I was listening as usual to the French Public Radio (France Inter) and at some point heard the short [10mn] Périphéries that gives every weekend an insight on the suburbs [on the “other side’ of the Parisian Périphérique boulevard]. The idea proposed by a geographer from Montpellier, Emmanuel Vigneron, was to point out the health inequalities between the wealthy 5th arrondissement of Paris and the not-so-far-away suburbs, by following the RER B train line from Luxembourg to La Plaine-Stade de France…

The disparities between the heart of Paris and some suburbs are numerous and massive, actually the more one gets away from the lifeline represented by the RER A and RER B train lines, so far from me the idea of negating this opposition, but the presentation made during those 10 minutes of Périphéries was quite approximative in statistical terms. For instance, the mortality rate in La Plaine is 30% higher than the mortality rate in Luxembourg and this was translated into the chances for a given individual from La Plaine to die in the coming year are 30% higher than if he [or she] lives in Luxembourg. Then a few minutes later the chances for a given individual from Luxembourg to die are 30% lower than he [or she] lives in La Plaine…. Reading from the above map, it appears that the reference is the mortality rate for the Greater Paris. (Those are 2010 figures.) This opposition that Vigneron attributes to a different access to health facilities, like the number of medical general practitioners per inhabitant, does not account for the huge socio-demographic differences between both places, for instance the much younger and maybe larger population in suburbs like La Plaine. And for other confounding factors: see, e.g., the equally large difference between the neighbouring stations of Luxembourg and Saint-Michel. There is no socio-demographic difference and the accessibility of health services is about the same. Or the similar opposition between the southern suburban stops of Bagneux and [my local] Bourg-la-Reine, with the same access to health services… Or yet again the massive decrease in the Yvette valley near Orsay. The analysis is thus statistically poor and somewhat ideologically biased in that I am unsure the data discussed during this radio show tells us much more than the sad fact that suburbs with less favoured populations show a higher mortality rate.

from my office

Posted in pictures with tags , , , , , on July 10, 2013 by xi'an

 

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