## ISBA 2021.1

Posted in Kids, Mountains, pictures, Running, Statistics, Travel, University life, Wines with tags , , , , , , , , , , , , , , , , , , on June 29, 2021 by xi'an

## simulation fodder for future exams

Posted in Books, Kids, R, Statistics with tags , , , , on February 20, 2019 by xi'an

Here are two nice exercises for a future simulation exam, seen and solved on X validated.The first one is about simulating a Gibbs sampler associated with the joint target

exp{-|x|-|y|-a|y-x|}

defined over IR² for a≥0 (or possibly a>-1). The conditionals are identical and non-standard, but a simple bound on the conditional density is the corresponding standard double exponential density, which makes for a straightforward accept-reject implementation. However it is also feasible to break the full conditional into three parts, depending on the respective positions of x, y, and 0, and to obtain easily invertible cdfs on the three intervals.The second exercise is about simulating from the cdf

$F(x)=1-\exp\{-ax-bx^{p+1}/(p+1)\}$

which can be numerically inverted. It is however more fun to call for an accept-reject algorithm by bounding the density with a ½ ½ mixture of an Exponential Exp(a) and of the 1/(p+1)-th power of an Exponential Exp(b/(p+1)). Since no extra constant appears in the solution,  I suspect the (p+1) in b/(p+1) was introduced on purpose. As seen in the above fit for 10⁶ simulations (and a=1,b=2,p=3), there is no deviation from the target! There is nonetheless an even simpler and rather elegant resolution to the exercise: since the tail function (1-F(x)) appears as the product of two tail functions, exp(-ax) and the other one, the cdf is the distribution of the minimum of two random variates, one with the Exp(a) distribution and the other one being the 1/(p+1)-th power of an Exponential Exp(b/(p+1)) distribution. Which of course returns a very similar histogram fit:

## alternatives to EM

Posted in Books, Statistics with tags , , , , , , , on January 30, 2019 by xi'an

In an arXived preprint submitted to Computational Statistics & Data Analysis, Chan, Han, and Lim study alternatives to EM for latent class models. That is, mixtures of products of Multinomials. (First occurrence of an indicator function being called the “Iverson bracket function”!) The introduction is fairly extensive given this most studied model. The criticisms of EM laid by the authors are that (a) it does not produce an evaluation of the estimation error, which does not sound correct; (b) the convergence is slow, which is also rather misleading as my [low dimensional] experience with mixtures is that it gets very quickly and apparently linearly  to the vicinity of one of the modes. The argument in favour of alternative non-linear optimisation approaches is that they can achieve quadratic convergence. One solution is a projected Quasi-Newton method, based on a quadratic approximation to the target. With some additional intricacies that make the claim of being “way easier than EM algorithm” somewhat specious. The second approach proposed in the paper is sequential quadratic programming, which incorporates the Lagrange multiplier in the target. While the different simulations in the paper show that EM may indeed call for a much larger number of iterations, the obtained likelihoods all are comparable.

## Big Bayes goes South

Posted in Books, Mountains, pictures, Running, Statistics, Travel, University life with tags , , , , , , , , , , , , , , , , , , , , , , on December 5, 2018 by xi'an

At the Big [Data] Bayes conference this week [which I found quite exciting despite a few last minute cancellations by speakers] there were a lot of clustering talks including the ones by Amy Herring (Duke), using a notion of centering that should soon appear on arXiv. By Peter Müller (UT, Austin) towards handling large datasets. Based on a predictive recursion that takes one value at a time, unsurprisingly similar to the update of Dirichlet process mixtures. (Inspired by a 1998 paper by Michael Newton and co-authors.) The recursion doubles in size at each observation, requiring culling of negligible components. Order matters? Links with Malsiner-Walli et al. (2017) mixtures of mixtures. Also talks by Antonio Lijoi and Igor Pruenster (Boconni Milano) on completely random measures that are used in creating clusters. And by Sylvia Frühwirth-Schnatter (WU Wien) on creating clusters for the Austrian labor market of the impact of company closure. And by Gregor Kastner (WU Wien) on multivariate factor stochastic models, with a video of a large covariance matrix evolving over time and catching economic crises. And by David Dunson (Duke) on distance clustering. Reflecting like myself on the definitely ill-defined nature of the [clustering] object. As the sample size increases, spurious clusters appear. (Which reminded me of a disagreement I had had with David McKay at an ICMS conference on mixtures twenty years ago.) Making me realise I missed the recent JASA paper by Miller and Dunson on that perspective.

Some further snapshots (with short comments visible by hovering on the picture) of a very high quality meeting [says one of the organisers!]. Following suggestions from several participants, it would be great to hold another meeting at CIRM in a near future. Continue reading

## JSM 2018 [#4]

Posted in Mountains, Statistics, Travel, University life with tags , , , , , , , , , , , , , , on August 3, 2018 by xi'an

As last ½ day of sessions at JSM2018 in an almost deserted conference centre, with a first session set together by Mario Peruggia and a second on Advances in Bayesian Nonparametric Modeling and Computation for Complex Data. Here are the slides of my talk this morning in the Bayesian mixture estimation session.

which I updated last night (Slideshare most absurdly does not let you update versions!)

Since I missed the COPSS Award ceremony for a barbecue with friends on Locarno Beach, I only discovered this morning that the winner this year is Richard Samworth, from Cambridge University, who eminently deserves this recognition, if only because of his contributions to journal editing, as I can attest from my years with JRSS B. Congrats to him as well as to Bin Yu and Susan Murphy for their E.L. Scott and R.A. Fisher Awards!  I also found out from an email to JSM participants that the next edition is in Denver, Colorado, which I visited only once in 1993 on a trip to Fort Collins visiting Kerrie Mengersen and Richard Tweedie. Given the proximity to the Rockies, I am thinking of submitting an invited session on ABC issues, which were not particularly well covered by this edition of JSM. (Feel free to contact me if you are interested in joining the session.)