## Slices and crumbs [arXiv:1011.4722]

Posted in Books, R, Statistics with tags , , , , , , , on November 30, 2010 by xi'an

An interesting note was arXived a few days ago by Madeleine Thompson and Radford Neal. Beside the nice touch of mixing crumbs and slices, the neat idea is to have multiple-try proposals for simulating within a slice and to decrease the dimension of the simulation space at each try. This dimension diminution is achieved via the construction of an orthogonal basis based on the gradient of the log densities at previously-rejected proposals.

$\mathbf{J}=(\nabla\log f(x_1),\ldots,\nabla\log f(x_k))$

until all dimensions are exhausted, in which case the scale of the Gaussian proposal is reduced. (The paper comes with R and C codes.) Provided the gradient can be computed (or at least approximated), this is a fairly general method (even though I have not tested it so cannot say how much calibration it requires). An interesting point is that, contrariwise to the delayed-rejection method of Antonietta Mira and co-authors,  the repeated proposals do not induce a complexification in the slice acceptance probability. I am less convinced by the authors’ conclusion that the method compares with adaptive Metropolis techniques, in the sense the “shrinking rank” method forgets about past experiences as it starts from scratch at each iteration: it is thus not really learning… (Now, in terms of performances, this may be the case!)

## Computing evidence

Posted in Books, R, Statistics with tags , , , , , , , , , , on November 29, 2010 by xi'an

The book Random effects and latent variable model selection, edited by David Dunson in 2008 as a Springer Lecture Note. contains several chapters dealing with evidence approximation in mixed effect models. (Incidentally, I would be interested in the story behind the  Lecture Note as I found no explanation in the backcover or in the preface. Some chapters but not all refer to a SAMSI workshop on model uncertainty…) The final chapter written by Joyee Ghosh and David Dunson (similar to a corresponding paper in JCGS) contains in particular the interesting identity that the Bayes factor opposing model h to model h-1 can be unbiasedly approximated by (the average of the terms)

$\dfrac{f(x|\theta_{i,h},\mathfrak{M}=h-1)}{f(x|\theta_{i,h},\mathfrak{M}=h)}$

when

• $\mathfrak{M}$ is the model index,
• the $\theta_{i,h}$‘s are simulated from the posterior under model h,
• the model $\mathfrak{M}=h-1$ only considers the h-1 first components of $\theta_{i,h}$,
• the prior under model h-1 is the projection of the prior under model h. (Note that this marginalisation is not the projection used in Bayesian Core.)

## home 3-0 pigeon

Posted in pictures with tags , on November 28, 2010 by xi'an

This is getting into a kind of custom: on each year at this time, a pigeon crashes into one of the windows of our house and the crash leaves an imprint that I always find impressive as a sort of ultimate picture! (This happened in 2008 and 2009, hence the title.) This year, I did not hear the crash nor did I find any trace of the poor bird so it either survived the crash or got eaten by a cat, feathers and all…. The picture is not as impressive as in 2008 (or as in this Flickr picture), which may explain for the softer hit!

## Puhdistus

Posted in Books with tags , , , , , on November 28, 2010 by xi'an

I read Purge (Puhdistus in Finnish) by Sofi Oksonen (in French) this summer when flying to San Francisco from Vancouver. This is a strong and gripping novel, as others have noticed before me. It takes place in post-communist Estonia where a widow of a (very lower-ranking) member of the communist nomenklatura is forced into considering her past choices and the lies she made to herself and to others when her grand-niece pops in, pursued by Russian-mafia-style gangsters who had enslaved her into a cruel prostitution scheme in Germany… This may sound like a cheap plot but the slow unravelling of the old woman’s (horrific) deeds and of the compromises she was led to endure makes for a much deeper read. There is also an historical level about Estonia being as ruthlessly occupied by Soviet soldiers as by Nazis, and about the hopeless fight of the local partisans followed by massive deportations to the Russian Far East. The book is thus multifaceted and the end, although predictable, is a nice tale of redemption for the old Aliide Truu who would otherwise appear as a remorseless criminal… An impressive and recommended tour-de-force! (Note that, despite some misguided criticisms found on Amazon, this is not a thriller!)

Purge
by Sofi Oksanen
Old Aliide Truu lives alone in a cottage in the woods, pestered by flies she wishes would leave her in peace. Her isolation is interrupted when she spies a young woman under a tree in her garden. The girl is strange; arriving in the dead of night, bruised, dirty and shoeless – why is she at Aliide’s door? Overcome by curiosity the old woman decides, warily, to take her in. Zara is on the run from men who tortured, raped, and sold her into slavery. Her only possession is a tattered photograph of her grandmother and another woman; in which Aliide recognizes herself and her sister. Horrified, she begins to realize that the past she has long tried to forget has finally caught up with her – Purge is a hauntingly intimate portrait of one family’s shame against a backdrop of European war. It is a fiercely compelling novel about what we will accept just to survive and the legacies created by our worst experiences.

## First snow

Posted in pictures with tags , , on November 27, 2010 by xi'an