Archive for Monte Carlo methods

Statistics slides (3)

Posted in Books, Kids, Statistics, University life with tags , , , , , , , , , , on October 9, 2014 by xi'an

La Défense from Paris-Dauphine, Nov. 15, 2012Here is the third set of slides for my third year statistics course. Nothing out of the ordinary, but the opportunity to link statistics and simulation for students not yet exposed to Monte Carlo methods. (No ABC yet, but who knows?, I may use ABC as an entry to Bayesian statistics, following Don Rubin’s example! Surprising typo on the Project Euclid page for this 1984 paper, by the way…) On Monday, I had the pleasant surprise to see Shravan Vasishth in the audience, as he is visiting Université Denis Diderot (Paris 7) this month.

Monte Carlo simulation and resampling methods for social science [book review]

Posted in Books, Kids, R, Statistics, University life with tags , , , , , , on October 6, 2014 by xi'an

Monte Carlo simulation and resampling methods for social science is a short paperback written by Thomas Carsey and Jeffrey Harden on the use of Monte Carlo simulation to evaluate the adequacy of a model and the impact of assumptions behind this model. I picked it in the library the other day and browse through the chapters during one of my métro rides. Definitely not an in-depth reading, so be warned!

Overall, I think the book is doing a good job of advocating the use of simulation to evaluate the pros and cons of a given model (rephrased as data generating process) when faced with data. And doing it in R. After some rudiments in probability theory and in R programming, it briefly explains the use of resident random generators if not of how to handle new distributions and then spend a large part of the book on simulation around generalised and regular linear models. For instance, in the linear model, the authors test the impact of heterocedasticity, multicollinearity, measurement error, omitted variable(s), serial correlation, clustered data, and heavy-tailed errors. While this is a perfect way of exploring those semi-hidden hypotheses behind the linear model, I wonder at the impact on students of this exploration. On the one hand, they will perceive the importance of those assumptions and hopefully remember them. On the other hand, and this is a very recurrent criticism of mine, this implies a lot of maturity from the students, i.e., they have to distinguish the data, the model [maybe] behind the data, the finite if large number of hypotheses one can test, and the interpretation of the outcome of a simulation test… Given that they were introduced to basic probability just a few chapters before, this expectation [from the students] may prove unrealistic. (And a similar criticism applies to the following chapters, from GLM to jackknife and bootstrap.)

At the end of the book, the authors ask the question as to how could a reader use the information in this book towards one’s work. Drafting a generic protocol for this reader, who is supposed to consider “alterations to the data generating process” (p.272) and to “identify a possible problem or assumption violation” (p.271). Thus requiring a readership “who has some training in quantitative methods” (p.1). And then some more. But I definitely sympathise with the goal of confronting models and theory with the harsh reality of simulation output!

plenty of new arXivals!

Posted in Statistics, University life with tags , , , , , on October 2, 2014 by xi'an

Here are some entries I spotted in the past days as of potential interest, for which I will have not enough time to comment:

  • arXiv:1410.0163: Instrumental Variables: An Econometrician’s Perspective by Guido Imbens
  • arXiv:1410.0123: Deep Tempering by Guillaume Desjardins, Heng Luo, Aaron Courville, Yoshua Bengio
  • arXiv:1410.0255: Variance reduction for irreversible Langevin samplers and diffusion on graphs by Luc Rey-Bellet, Konstantinos Spiliopoulos
  • arXiv:1409.8502: Combining Particle MCMC with Rao-Blackwellized Monte Carlo Data Association for Parameter Estimation in Multiple Target Tracking by Juho Kokkala, Simo Särkkä
  • arXiv:1409.8185: Adaptive Low-Complexity Sequential Inference for Dirichlet Process Mixture Models by Theodoros Tsiligkaridis, Keith W. Forsythe
  • arXiv:1409.7986: Hypothesis testing for Markov chain Monte Carlo by Benjamin M. Gyori, Daniel Paulin
  • arXiv:1409.7672: Order-invariant prior specification in Bayesian factor analysis by Dennis Leung, Mathias Drton
  • arXiv:1409.7458: Beyond Maximum Likelihood: from Theory to Practice by Jiantao Jiao, Kartik Venkat, Yanjun Han, Tsachy Weissman
  • arXiv:1409.7419: Identifying the number of clusters in discrete mixture models by Cláudia Silvestre, Margarida G. M. S. Cardoso, Mário A. T. Figueiredo
  • arXiv:1409.7287: Identification of jump Markov linear models using particle filters by Andreas Svensson, Thomas B. Schön, Fredrik Lindsten
  • arXiv:1409.7074: Variational Pseudolikelihood for Regularized Ising Inference by Charles K. Fisher

vector quantile regression

Posted in pictures, Statistics, University life with tags , , , , , , , on July 4, 2014 by xi'an

My Paris-Dauphine colleague Guillaume Carlier recently arXived a statistics paper entitled Vector quantile regression, co-written with Chernozhukov and Galichon. I was most curious to read the paper as Guillaume is primarily a mathematical analyst working on optimisation problems like optimal transport. And also because I find quantile regression difficult to fathom as a statistical problem. (As it happens, both his co-authors are from econometrics.) The results in the paper are (i) to show that a d-dimensional (Lebesgue) absolutely continuous random variable Y can always be represented as the deterministic transform Y=Q(U), where U is a d-dimensional [0,1] uniform (the paper expresses this transform as conditional on a set of regressors Z, but those essentially play no role) and Q is monotonous in the sense of being the gradient of a convex function,

Q(u) = \nabla q(u) and \{Q(u)-Q(v)\}^\text{T}(u-v)\ge 0;

(ii) to deduce from this representation a unique notion of multivariate quantile function; and (iii) to consider the special case when the quantile function Q can be written as the linear

\beta(U)^\text{T}Z

where β(U) is a matrix. Hence leading to an estimation problem.

While unsurprising from a measure theoretic viewpoint, the representation theorem (i) is most interesting both for statistical and simulation reasons. Provided the function Q can be easily estimated and derived, respectively. The paper however does not provide a constructive tool for this derivation, besides indicating several characterisations as solutions of optimisation problems. From a statistical perspective, a non-parametric estimation of  β(.) would have useful implications in multivariate regression, although the paper only considers the specific linear case above. Which solution is obtained by a discretisation of all variables and  linear programming.

Statistical modeling and computation [apologies]

Posted in Books, R, Statistics, University life with tags , , , , , , , , , , , on June 11, 2014 by xi'an

In my book review of the recent book by Dirk Kroese and Joshua Chan,  Statistical Modeling and Computation, I mistakenly and persistently typed the name of the second author as Joshua Chen. This typo alas made it to the printed and on-line versions of the subsequent CHANCE 27(2) column. I am thus very much sorry for this mistake of mine and most sincerely apologise to the authors. Indeed, it always annoys me to have my name mistyped (usually as Roberts!) in references.  [If nothing else, this typo signals it is high time for a change of my prescription glasses.]

Statistical modeling and computation [book review]

Posted in Books, R, Statistics, University life with tags , , , , , , , , , , , , , on January 22, 2014 by xi'an

Dirk Kroese (from UQ, Brisbane) and Joshua Chan (from ANU, Canberra) just published a book entitled Statistical Modeling and Computation, distributed by Springer-Verlag (I cannot tell which series it is part of from the cover or frontpages…) The book is intended mostly for an undergrad audience (or for graduate students with no probability or statistics background). Given that prerequisite, Statistical Modeling and Computation is fairly standard in that it recalls probability basics, the principles of statistical inference, and classical parametric models. In a third part, the authors cover “advanced models” like generalised linear models, time series and state-space models. The specificity of the book lies in the inclusion of simulation methods, in particular MCMC methods, and illustrations by Matlab code boxes. (Codes that are available on the companion website, along with R translations.) It thus has a lot in common with our Bayesian Essentials with R, meaning that I am not the most appropriate or least unbiased reviewer for this book. Continue reading

MCQMC2014 in Belgium

Posted in Books, Statistics, Travel, University life with tags , , , , , , , , , on October 11, 2013 by xi'an

The conference MCQMC2014 (which stands for Monte Carlo and Quasi-Monte Carlo) will take place in Leuven, Belgium, on April 6-11. More exactly, in the Katholieke Universiteit Leuven, which is the Flemish-speaking side of the split (1968) Catholic University of Leuven, the French speaking side Université Catholique de Louvain being located in Louvain-la-Neuve. After missing MCQMC2012 in Sydney,  I will attend this conference where I give an invited talk (on ABC, what else..?!). As it happens (and kind of logically), I have visited Louvain-la-Neuve many times, especially in the previous era where historical Bayesians Michel Mouchard, Jean-Marie Rolin and Léopold Simar were together in the Statistics department—two of them contributing to the highly formalised “Elements of Bayesian Statistics” that I perused during my PhD thesis in Rouen—, but I have never been to Leuven or to KU Leuven,

A great item of news is that one of the two tutorials (on April 6, 2014) will given by Art Owen, the theme being “ANOVA, global sensitivity, Sobol’ indices and all that“, The second tutorial is by Mike Giles (Oxford) on his approach of multi-level Monte Carlo methods. (If the organisers follow the MCQMC2012 trend, the Sunday afternoon tutorials should follow one another.)

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