Archive for April, 2011

Judge Dee

Posted in Books, Travel with tags , on April 30, 2011 by xi'an

A few weeks ago, I came across a book Dix petits démons chinois in the series Les nouvelles enquêtes du Juge Ti (The new cases of Judge Dee) by Frédéric Lenormand. As I highly enjoyed the original Judge Dee series by Robert van Gulik, I bought it. The style of this new book is rather far from the original and the detective plot is rather poor, so I do not think I will buy further books in the series. However, this started me on re-reading van Gulik’s books, which remain as enjoyable as I found them twenty-five years ago… Incidentally, a movie called Detective Dee just came out (in France) a few days ago. It again builds on the same historical Tang dynasty judge, with apparently little connection with the original books.

A domino formula for Bayes factors

Posted in Statistics with tags , , , on April 29, 2011 by xi'an

This afternoon, when working on ABC with Jean-Marie Cornuet, I came up with a domino formula for Bayes factors. It goes like this

B_{12}(x_1,\ldots,x_n) = \dfrac{\mathbb{E}^{\pi_1}[f_1(x_n|\theta_1)|x_1,\ldots,x_{n-1}]}{\mathbb{E}^{\pi_2}[f_2(x_n|\theta_2)|x_1,\ldots,x_{n-1}]} \times

\times \cdots\times\dfrac{\mathbb{E}^{\pi_1}[f_1(x_2|\theta_1)|x_1]}{\mathbb{E}^{\pi_2}[f_2(x_2|\theta_2)|x_1]} \times\dfrac{\mathbb{E}^{\pi_1}[f_1(x_1|\theta_1)]}{\mathbb{E}^{\pi_2}[f_2(x_1|\theta_2)]}

with hopefully clear if implicit notations. I wonder if this has been exploited previously for computational purposes as each expectation is taken under the “previous” posterior: it could have an appeal from a sequential Monte Carlo perspective.

Bayesian conference in 上海 [O'Bayes 2011]

Posted in Statistics, Travel, University life with tags , , , , , on April 29, 2011 by xi'an

Just to remind ‘Og‘s readers that the 2011 International Workshop on Objective Bayes Methodology will take place on June 11-15th 2011 at East China Normal University  (Putuo Campus), Shanghai (上海), China. The deadline for early registration has been extended till May 10. This should be a wonderful opportunity to exchange about the latest in objective Bayes methodology, to meet Chinese Bayesians and to discover that part of China. (Actually, there is a possibility of an excursion to Guilin, Xi’an and Beijing after the meeting!) Here is a picture of my visa, received today.

Is Bayes posterior [quick and] dirty?!

Posted in Books, Statistics, University life with tags , , , , on April 28, 2011 by xi'an

I have been asked to discuss the on-coming Statistical Science paper by Don Fraser, Is Bayes posterior quick and dirty confidence?.  The title was intriguing if clearly provocative and so did I read through the whole paper… (The following is a draft of my discussion.)

The central point in Don’s paper seems to be a demonstration that Bayes confidence sets are not valid because they do not provide the proper frequentist coverage. While I appreciate the effort made therein of evaluating Bayesian bounds in a frequentist light, and while Don’s paper does shed new insight on the evaluation of Bayesian bounds in a frequentist light, the main point of the paper seems to be a radical reexamination of the relevance of the whole Bayesian approach to confidence regions. The outcome is rather surprising in that the disagreement between classical and frequentist perspectives is usually quite limited [in contrast with tests] in that the coverage statements agree to orders between n^{-1/2} and n^{-1}, following older results by Welch and Peers (1963). Continue reading

Mixtures: Estimation and Applications out!

Posted in Books, Statistics, University life with tags , , , , on April 27, 2011 by xi'an

The book I co-edited with Kerrie Mengersen and Mike Titterington, Mixture: Estimation and Applications, has just been published by Wiley! It is a pleasure to flip through the chapters contributed by the participants to the ICMS workshop of about a year ago in Edinburgh. While there may (must) be residual typos, I did not spot any obvious mishap in the production of figures and Buachaille Etive Beag proudly stands on the cover (despite contrary advice from some ‘Og readers). It is also a pleasure to have this book published in the same series as references like Titterington, Smith and Makov’s Statistical Analysis of Finite Mixture Distributions, and McLachlan and Peel’s Finite Mixture Model.  (The “product description” on amazon does not start very well, though: “This book uses the EM (expectation maximization) algorithm to simultaneously estimate the missing data and unknown parameter(s) associated with a data set. The parameters describe the component distributions of the mixture; the distributions may be continuous or discrete.” It fortunately improves by reproducing the back cover.)

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