Archive for computational statistics

new kid on the blog

Posted in Kids, Statistics, University life with tags , , , , , , on January 27, 2016 by xi'an

[I first thought this title was highly original but a google search showed me wrong…] This short post to point out to the new blog started by Ingmar Schuster on computational statistics and linguistics. Which, so far, keeps strictly to the discussion of recent research papers (rather than ratiocinating about all kinds of tangential topics like a certain ‘Og…) Some of which we may discuss in parallel. And some not. So keep posted! Ingmar came to Paris-Dauphine for a doctoral visit last Winter and is back as a postdoc (supported by the Fondation des Sciences Mathématiques de Paris) since last Fall. Working with me and Nicolas, among others.

 

done! [#2]

Posted in Kids, Statistics, University life with tags , , , , , , , , , on January 21, 2016 by xi'an

exosPhew! I just finished my enormous pile of homeworks for the computational statistics course… This massive pile is due to an unexpected number of students registering for the Data Science Master at ENSAE and Paris-Dauphine. As I was not aware of this surge, I kept to my practice of asking students to hand back solved exercises from Monte Carlo Statistical Methods at the beginning of each class. And could not change the rules of the game once the course had started! Next year, I’ll make sure to get some backup for grading those exercises. Or go for group projects instead…

reaching transcendence for Gaussian mixtures

Posted in Books, R, Statistics with tags , , , , on September 3, 2015 by xi'an

Nested sampling sample on top of a mixture log-likelihood“…likelihood inference is in a fundamental way more complicated than the classical method of moments.”

Carlos Amendola, Mathias Drton, and Bernd Sturmfels arXived a paper this Friday on “maximum likelihood estimates for Gaussian mixtures are transcendental”. By which they mean that trying to solve the five likelihood equations for a two-component Gaussian mixture does not lead to an algebraic function of the data. (When excluding the trivial global maxima spiking at any observation.) This is not highly surprising when considering two observations, 0 and x, from a mixture of N(0,1/2) and N(μ,1/2) because the likelihood equation

(x-\mu)\exp\{\mu^2\}-x+\mu\exp\{-\mu(2x-\mu)\}=0

involves both exponential and algebraic terms. While this is not directly impacting (statistical) inference, this result has the computational consequence that the number of critical points ‘and also the maximum number of local maxima, depends on the sample size and increases beyond any bound’, which means that EM faces increasing difficulties in finding a global finite maximum as the sample size increases…

Bayesian model averaging in astrophysics

Posted in Books, Statistics, University life with tags , , , , , , , , , , on July 29, 2015 by xi'an

[A 2013 post that somewhat got lost in a pile of postponed entries and referee’s reports…]

In this review paper, now published in Statistical Analysis and Data Mining 6, 3 (2013), David Parkinson and Andrew R. Liddle go over the (Bayesian) model selection and model averaging perspectives. Their argument in favour of model averaging is that model selection via Bayes factors may simply be too inconclusive to favour one model and only one model. While this is a correct perspective, this is about it for the theoretical background provided therein. The authors then move to the computational aspects and the first difficulty is their approximation (6) to the evidence

P(D|M) = E \approx \frac{1}{n} \sum_{i=1}^n L(\theta_i)Pr(\theta_i)\, ,

where they average the likelihood x prior terms over simulations from the posterior, which does not provide a valid (either unbiased or converging) approximation. They surprisingly fail to account for the huge statistical literature on evidence and Bayes factor approximation, incl. Chen, Shao and Ibrahim (2000). Which covers earlier developments like bridge sampling (Gelman and Meng, 1998).

As often the case in astrophysics, at least since 2007, the authors’ description of nested sampling drifts away from perceiving it as a regular Monte Carlo technique, with the same convergence speed n1/2 as other Monte Carlo techniques and the same dependence on dimension. It is certainly not the only simulation method where the produced “samples, as well as contributing to the evidence integral, can also be used as posterior samples.” The authors then move to “population Monte Carlo [which] is an adaptive form of importance sampling designed to give a good estimate of the evidence”, a particularly restrictive description of a generic adaptive importance sampling method (Cappé et al., 2004). The approximation of the evidence (9) based on PMC also seems invalid:

E \approx \frac{1}{n} \sum_{i=1}^n \dfrac{L(\theta_i)}{q(\theta_i)}\, ,

is missing the prior in the numerator. (The switch from θ in Section 3.1 to X in Section 3.4 is  confusing.) Further, the sentence “PMC gives an unbiased estimator of the evidence in a very small number of such iterations” is misleading in that PMC is unbiased at each iteration. Reversible jump is not described at all (the supposedly higher efficiency of this algorithm is far from guaranteed when facing a small number of models, which is the case here, since the moves between models are governed by a random walk and the acceptance probabilities can be quite low).

The second quite unrelated part of the paper covers published applications in astrophysics. Unrelated because the three different methods exposed in the first part are not compared on the same dataset. Model averaging is obviously based on a computational device that explores the posteriors of the different models under comparison (or, rather, averaging), however no recommendation is found in the paper as to efficiently implement the averaging or anything of the kind. In conclusion, I thus find this review somehow anticlimactic.

Bayesian computation: a summary of the current state, and samples backwards and forwards

Posted in Books, Statistics, University life with tags , , , , , , , , on June 25, 2015 by xi'an

“The Statistics and Computing journal gratefully acknowledges the contributions for this special issue, celebrating 25 years of publication. In the past 25 years, the journal has published innovative, distinguished research by leading scholars and professionals. Papers have been read by thousands of researchers world-wide, demonstrating the global importance of this field. The Statistics and Computing journal looks forward to many more years of exciting research as the field continues to expand.” Mark Girolami, Editor in Chief for The Statistics and Computing journal

Our joint [Peter Green, Krzysztof Łatuszyński, Marcelo Pereyra, and myself] review [open access!] on the important features of Bayesian computation has already appeared in the special 25th anniversary issue of Statistics & Computing! Along with the following papers

which means very good company, indeed! And happy B’day to Statistics & Computing!

postdoc in the Alps

Posted in Kids, Mountains, Statistics, Travel, University life with tags , , , , , , , , , on May 22, 2015 by xi'an

Post-doctoral Position in Spatial/Computational Statistics (Grenoble, France)

A post-doctoral position is available in Grenoble, France, to work on computational methods for spatial point process models. The candidate will work with Simon Barthelmé (GIPSA-lab, CNRS) and Jean-François Coeurjolly (Univ. Grenoble Alpes, Laboratory Jean Kuntzmann) on extending point process methodology to deal with large datasets involving multiple sources of variation. We will focus on eye movement data, a new and exciting application area for spatial statistics. The work will take place in the context of an interdisciplinary project on eye movement modelling involving psychologists, statisticians and applied mathematicians from three different institutes in Grenoble.

The ideal candidate has a background in spatial or computational statistics or machine learning. Knowledge of R (and in particular the package spatstat) and previous experience with point process models is a definite plus.

The duration of the contract is 12+6 months, starting 01.10.2015 at the earliest. Salary is according to standard CNRS scale (roughly EUR 2k/month).

Grenoble is the largest city in the French Alps, with a very strong science and technology cluster. It is a pleasant place to live, in an exceptional mountain environment.

I am cold all over…

Posted in Books, Kids, Statistics, University life with tags , , , , , , , on October 29, 2014 by xi'an

unusual snowfall on Bois de Boulogne, March 12, 2013An email from one of my Master students who sent his problem sheet (taken from Monte Carlo Statistical Methods) late:

Bonsoir Professeur
Je « suis » votre cours du mercredi dont le formalisme mathématique me fait froid partout
Avec beaucoup de difficulté je vous envoie mes exercices du premier chapitre de votre livre.

which translates as

Good evening Professor,
I “follow” your Wednesday class which mathematical formalism makes me cold all over. With much hardship, I send you the first batch of problems from your book.

I know that winter is coming, but, still, making students shudder from mathematical cold is not my primary goal when teaching Monte Carlo methods!