## Versailles by night

Posted in Travel with tags , , on July 31, 2009 by xi'an

A few weeks ago, we went with a very good friend to the light and watermusic evening show in the Versailles palace (which takes place most of the summer). Here are a few pictures taken by my daughter. Although there is a “tourist-trap” feeling in the show (and the place is literarly crawling with people and nationalities!), the overall harmony and order of the Le Notre gardens eventually overcome this unpleasant aspect. As the night comes in, especially on a clean windless evening, the crowd somewhat vanishes and all that remains are the fountains, the gardens, and the castle in the background.

Even the fireworks that close the evening are enjoyable (and I usually hate fireworks for their noise and vacuity!) because they were already part of the parties at the time Versailles was inhabited…

## Harmonic mean estimators

Posted in Statistics with tags , , , on July 30, 2009 by xi'an

In connection with my recent talk at MaxEnt 2009 and older talks and posts, I have just written with Darren Wraith a very short note on some computational methods used for approximating Bayes factors. This note has now been arXived and it is strongly based on the slides for this talk. Nonetheless, I think there is an interesting point made in the section on harmonic mean estimators, namely that (a) using an MCMC output, it is easy to determine highest posterior density regions by looking directly at the numerical value of the posterior (up to a constant) and (b) those HPD regions can be used to construct pseudo-proposals whose support is one of those regions. This cancels the infinite variance difficulty rightly stressed recently by Radford Neal. In short, the fact that

$\mathbb{E}\left[ \dfrac{\varphi(\theta)}{\pi(\theta) L(\theta|x)} \mid x \right] = \dfrac{1}{m(x)}$

holds for any density φ is of interest for approximating m(x) and therefore Bayes factors only when φ is such that the corresponding importance sampling estimator has a finite variance. The infamous but common choice φ=π is rarely appropriate in this regard. However, if one uses the output of an MCMC sampler to determine an empirical highest posterior density region, restricting φ to this region or to an approximation of it—like an ellipsoid—escapes the infinite variance difficulties.

## IMS membership is free

Posted in Statistics, University life with tags , , on July 29, 2009 by xi'an

As recalled in the IMS Bulletin I received yesterday, IMS membership is free for students and it includes a free print journal subscription! This means getting the Annals of Statistics for free! Or the Annals of Applied Statistics or yet the Annals of Applied Probability… And all of them as electronic versions. I detailed in this Christmas post the reasons why I thought joining one or several statistical societies was important. Already pointing out the free feature for IMS membership! So, if you are a student or if you teach or supervise students in statistics, probability or related fields, make sure you take advantage of this opportunity.

## Little bonsai [of the latter days]

Posted in Kids on July 28, 2009 by xi'an

The remaining bonsai is on the exit lane… It has not recovered from its week outside and the roots have started to rot. We may resume the experiment in the Fall with new seeds, stay tuned!

## Aosta [hike 3.2]

Posted in Mountains, Travel with tags , , on July 27, 2009 by xi'an

We have received in the mail this weekend a cd of the pictures taken by our mountain guide Abele Blanc during the hike last week and they are superb, like the one above of the Parnassius Apollo butterfly, which is one of the emblems of the Gran Paradiso National Park and which mostly dwells in Aosta and in the nearby Valais.