## George’s dream

Posted in Kids, Travel with tags , , , , , on April 11, 2015 by xi'an

While I have shared this idea with many of my friends [in both senses that I mentioned it and that they shared the same feeling that it would be a great improvement], the first time I heard of the notion was in George Casella‘s kitchen in Ithaca, New York, in the early 1990’s… We were emptying the dishwasher together and George was reflecting that it would be so convenient to have a double dishwasher and remove the need to empty it altogether! Although, at the moral level, I think that we should do without dishwashers, I found this was a terrific idea and must have told the joke to most of my friends. I was nonetheless quite surprised and very pleased to receive the news from Nicole today that Fisher & Paykel (from Auckland, New Zealand) had gone all the way to produce a double dishwasher, or more exactly a double dishdrawer, perfectly suited to George’s wishes! (Pleased that she remembered the notion after all those years, not pleased with the prospect of buying a double dish washer for more than double the cost of [and a smaller volume than] a regular dishwasher!)

## an email exchange about integral representations

Posted in Books, R, Statistics, University life with tags , , , , on April 8, 2015 by xi'an

I had an interesting email exchange [or rather exchange of emails] with a (German) reader of Introducing Monte Carlo Methods with R in the past days, as he had difficulties with the validation of the accept-reject algorithm via the integral

$\mathbb{P}(Y\in \mathcal{A},U\le f(Y)/Mg(Y)) = \int_\mathcal{A} \int_0^{f(y)/Mg(y)}\,\text{d}u\,g(y)\,\text{d}y\,,$

in that it took me several iterations [as shown in the above] to realise the issue was with the notation

$\int_0^a \,\text{d}u\,,$

which seemed to be missing a density term or, in other words, be different from

$\int_0^1 \,\mathbb{I}_{(0,a)}(u)\,\text{d}u\,,$

What is surprising for me is that the integral

$\int_0^a \,\text{d}u$

has a clear meaning as a Riemann integral, hence should be more intuitive….

## which parameters are U-estimable?

Posted in Books, Kids, Statistics, University life with tags , , , , , , , on January 13, 2015 by xi'an

Today (01/06) was a double epiphany in that I realised that one of my long-time beliefs about unbiased estimators did not hold. Indeed, when checking on Cross Validated, I found this question: For which distributions is there a closed-form unbiased estimator for the standard deviation? And the presentation includes the normal case for which indeed there exists an unbiased estimator of σ, namely

$\frac{\Gamma(\{n-1\}/{2})}{\Gamma({n}/{2})}2^{-1/2}\sqrt{\sum_{k=1}^n(x_i-\bar{x})^2}$

which derives directly from the chi-square distribution of the sum of squares divided by σ². When thinking further about it, if a posteriori!, it is now fairly obvious given that σ is a scale parameter. Better, any power of σ can be similarly estimated in a unbiased manner, since

$\left\{\sum_{k=1}^n(x_i-\bar{x})^2\right\}^\alpha \propto\sigma^\alpha\,.$

And this property extends to all location-scale models.

So how on Earth was I so convinced that there was no unbiased estimator of σ?! I think it stems from reading too quickly a result in, I think, Lehmann and Casella, result due to Peter Bickel and Erich Lehmann that states that, for a convex family of distributions F, there exists an unbiased estimator of a functional q(F) (for a sample size n large enough) if and only if q(αF+(1-α)G) is a polynomial in 0α1. Because of this, I had this

impression that only polynomials of the natural parameters of exponential families can be estimated by unbiased estimators… Note that Bickel’s and Lehmann’s theorem does not apply to the problem here because the collection of Gaussian distributions is not convex (a mixture of Gaussians is not a Gaussian).

This leaves open the question as to which transforms of the parameter(s) are unbiasedly estimable (or U-estimable) for a given parametric family, like the normal N(μ,σ²). I checked in Lehmann’s first edition earlier today and could not find an answer, besides the definition of U-estimability. Not only the question is interesting per se but the answer could come to correct my long-going impression that unbiasedness is a rare event, i.e., that the collection of transforms of the model parameter that are U-estimable is a very small subset of the whole collection of transforms.

## O-Bayes15 [registration & call for papers]

Posted in Kids, pictures, Statistics, Travel, University life with tags , , , , , , , on January 5, 2015 by xi'an

Both registration and call for papers have now been posted on the webpage of the 11th International Workshop on Objective Bayes Methodology, aka O-Bayes 15, that will take place in Valencia next June 1-5.  The spectrum of the conference is quite wide, as reflected by the range of speakers. In addition, this conference is dedicated to our friend Susie Bayarri, to celebrate her life and contributions to Bayesian Statistics. And in continuation of the morning jog in the memory of George Casella organised by Laura Ventura in Padova, there will be a morning jog for Susie. So register for the meeting and bring your running shoes!

## back in Gainesville (FL)

Posted in pictures, Running, Statistics, Travel, University life, Wines with tags , , , , , , , , on November 12, 2014 by xi'an

Today, I am flying to Gainesville, Florida, for the rest of the week, to give a couple of lectures. More precisely, I have actually been nominated the 2014 Challis lecturer by the Department of Statistics there, following an impressive series of top statisticians (most of them close friends, is there a correlation there?!). I am quite excited to meet again with old friends and to be back at George’s University, if only for a little less than three days. (There is a certain trend in those Fall trips as I have been going for a few days and two talks to the USA or Canada for the past three Falls: to Ames and Chicago in 2012, to Pittsburgh (CMU) and Toronto in 2013…)

## no more car talk

Posted in Books, Kids, Travel with tags , , , , , on November 9, 2014 by xi'an

When I first came went to the US in 1987, I switched from listening to the French public radio to listening to NPR, the National Public Radio network. However, it was not until I met both George Casella and Bernhard Flury that I started listening to “Car Talk”, the Sunday morning talk-show by the Magliozzi brothers where listeners would call and expose their car problem and get jokes and sometime advice in reply. Both George and Bernhard were big fans of the show, much more for the unbelievable high spirits it provided than for any deep interest in mechanics. And indeed there was something of the spirit of Zen and the art of motorcycle maintenance in that show, namely that through mechanical issues, people would come to expose deeper worries that the Magliozzi brothers would help bring out, playing the role of garage-shack psychiatrists…Which made me listen to them, despite my complete lack of interest in car, mechanics and repair in general.

One of George’s moments of fame was when he wrote to the Magliozzi brothers about Monty Hall’s problem, because they had botched their explanation as to why one should always change door. And they read it on the air, with the line “Who is this Casella guy from Cornell University? A professor? A janitor?” since George had just signed George Casella, Cornell University. Besides, Bernhard was such a fan of the show that he taped every single morning show, that he would later replay on long car trips (I do not know how his familly enjoyed the exposure to the show, though!). And so happened to have this line about George on tape, that he sent him a few weeks later… I am reminiscing all this because I saw in the NYT today that the older brother, Tom Magliozzi, had just died. Some engines can alas not be fixed… But I am sure there will be a queue of former car addicts in some heavenly place eager to ask him their question about their favourite car. Thanks for the ride, Tom!

## hasta luego, Susie!

Posted in Statistics, University life with tags , , , , , , , , on August 20, 2014 by xi'an

I just heard that our dear, dear friend Susie Bayarri passed away early this morning, on August 19, in Valencià, Spain… I had known Susie for many, many years, our first meeting being in Purdue in 1987, and we shared many, many great times during simultaneous visits to Purdue University and Cornell University in the 1990’s. During a workshop in Cornell organised by George Casella (to become the unforgettable Camp Casella!), we shared a flat together and our common breakfasts led her to make fun of my abnormal consumption of cereals  forever after, a recurrent joke each time we met! Another time, we were coming from the movie theatre in Lafayette in Susie’ s car when we got stopped for going through a red light. Although she tried very hard, her humour and Spanish verve were for once insufficient to convince her interlocutor.

Susie was a great Bayesian, contributing to the foundations of Bayesian testing in her numerous papers and through the direction of deep PhD theses in Valencia. As well as to queuing systems and computer models. She was also incredibly active in ISBA, from the very start of the Bayesian society, and was one of the first ISBA presidents. She also definitely contributed to the Objective Bayes section of ISBA, especially in the construction of the O’Bayes meetings. She gave a great tutorial on Bayes factors at the last O’Bayes conference in Duke last December, full of jokes and passion, despite being already weak from her cancer…

So, hasta luego, Susie!, from all your friends. I know we shared the same attitude about our Catholic education and our first names heavily laden with religious meaning, but I’d still like to believe that your rich and contagious laugh now resonates throughout the cosmos. So, hasta luego, Susie, and un abrazo to all of us missing her.