Filed under: pictures, Travel Tagged: 10/10, abolition, death penalty ]]>

Filed under: Books, Kids Tagged: George Martin, Song of Ice and Fire ]]>

Filed under: pictures, Statistics, Travel, University life Tagged: Antarctica, Madrid, Spain ]]>

On a linear board of length 17, Alice and Bob set alternatively red and blue tokens. Two tokens of the same colour cannot sit next to one another. Devise a winning strategy for the first player.

**I**n the ‘Og tradition, this calls for a recurrent R code:

game=function(n=17,col=1,tak=rep(0,n)){ frei=rew=0*tak # stopping rule if (sum(tak==col)==0){ frei=(tak==0)}else{ for (i in (1:n)[tak!=-col]) frei[i]=(min(abs((1:n)[tak==col]-i))>1)} # left positions if (sum(frei)>0){ for (i in (1:n)[frei==1]){ prop=tak;prop[i]=col rew[i]=1-game(n=n,col=-col,tak=prop)}} # outcome of best choice return(max(rew))}

While I did not run the rudimentary recursive function for n=17, I got a zero return from n=2 till n=12, meaning that the starting player is always going to lose if the other player plays optimally.

Filed under: Books, Kids, Statistics, University life Tagged: Le Monde, mathematical puzzle, R, recursive function ]]>

Filed under: Books, Statistics, University life Tagged: accept-reject algorithm, ARS, BUGS, Gibbs sampler, Monte Carlo Statistical Methods, Wally Gilks ]]>

“Convergence was achieved in all cases, even when the starting values were poor and this emphasizes the numerical stability of the EM algorithm.” K. Adamidis

Adamidis then constructs an EM algorithm on the completed set of auxiliary variables with a closed form update on both parameters. Unfortunately, the algorithm only works when s²>x̄. Otherwise, it gets stuck at the boundary p=0 and N=∞. I was hoping for a replica of the mixture case where local maxima are more interesting than the degenerate global maximum… (Of course, there is always the alternative of using a Bayesian noninformative approach.)

Filed under: Books, Kids, Statistics, University life Tagged: Australian & New Zealand Journal of Statistics, compound Poisson distribution, cross validated, EM algorithm, John Kruschke, LSD, mixtures of distributions, negative binomial distribution ]]>

*“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.”*

**Y**esterday, 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.

Filed under: Books, Statistics, University life Tagged: Bayesian inference, boulevard périphérique, Francis Galton, HPD region, inverse cdf, Kullback-Leibler divergence, optimal transport, quincunx, Université Paris Dauphine ]]>

Filed under: pictures, Running Tagged: Argentan, cup, half-marathon, Normandy, race, Timex, veteran (V2) ]]>

Filed under: pictures, Travel Tagged: Alberta, Banff, Banff Centre, BIRS, Canada, Canadian Rockies, Fall ]]>

*“For example, a religiously affiliated college that receives federal grants could fire a professor simply for being gay and still receive those grants. Or federal workers could refuse to process the tax returns of same-sex couples simply because of bigotry against their marriages. It doesn’t stop there. As critics of the bill quickly pointed out, the measure’s broad language — which also protects those who believe that “sexual relations are properly reserved to” heterosexual marriages alone — would permit discrimination against anyone who has sexual relations outside such a marriage. That would appear to include women who have children outside of marriage, a class generally protected by federal law.” The New York Time
*

**A**n excerpt from this week New York Time Sunday Review editorial about what it qualifies as “a nasty bit of business congressional Republicans call the First Amendment Defense Act.” A bill which first line states to be intended to “prevent discriminatory treatment of any person on the basis of views held with respect to marriage” and which in essence would allow for discriminatory treatment of homosexual and unmarried couples not to be prosecuted. A fine example of Newspeak if any! (Maybe they could also borrow Orwell‘s notion of a Ministry of Love.) Another excerpt of the bill that similarly competes for Newspeak of the Year:

(5) Laws that protect the free exercise of religious beliefs and moral convictions about marriage will encourage private citizens and institutions to demonstrate tolerance for those beliefs and convictions and therefore contribute to a more respectful, diverse, and peaceful society.

This reminded me of a story I was recently told me about a friend of a friend who is currently employed by a Catholic school in Australia and is afraid of being fired if found being pregnant outside of marriage. Which kind of “freedom” is to be defended in such “tolerant” behaviours?!

Filed under: Kids, Travel Tagged: 1984, bigotry, discrimination, George Orwell, Newspeak, same-sex marriage, The New York Times ]]>