If the Dickey-Savage ratio does not hold…

or rather is arbitrary, then this should cause problems for methods, papers, and books that do use it, no…?! This is the question I got on Monday from an Og reader.

Actually, not necessarily: when looking for instance at O’Hagan and Forster’s Advanced Theory of Statistics 2B (2004, 7.16), the Bayes factor they construct in the model, when testing for , is correct for the same reason the “proof” of the Dickey-Savage ratio was accepted, namely the use of the “right” version of the conditional density. Similarly, when Chen, Shao and Ibrahim (2000, Section 5.10.3) introduce the ratio, and the Verdinelli-Wasserman (1996) generalisation, they implement the Monte Carlo approximation using a specific version of the full conditionals.

The plus of our perspective is therefore to give a general representation that does not involve unnatural constraints on the priors. The example below is taken from a probit example in the incoming note with Jean-Michel Marin, comparing the Dickey-Savage-like approximation to the Bayes factor with an harmonic mean version and the unbeatable Chib’s solution.

I nonetheless found [by Googling] one case where the Dickey-Savage ratio was leading to a definition problem, namely in a preprint posted by Wetzels, Grasman, and Wagenmakers,  where the authors derive the Bayes factor as the Dickey-Savage ratio under an encompassing prior constructed earlier by Klugkist et al. (2005), using a limiting argument via L’Hospital rule that seems equally contradictory with measure theoretic principles. Paradoxically, the authors mention the Borel-Kolmogorov paradox, i.e. the dependence on the conditioning σ-algebra, as a possible issue with their prior construction but, while their appendix A clearly concludes that the limit is arbitrary, they  still evacuate the issue of the choice of the version of the conditional density.

Introduction to Bayesian analysis

Yesterday, I started my standard master course on Bayesian analysis, based on my book The Bayesian Choice. Here are the slides (in English)

They definitely need to be upgraded into Beamer and enlarged to some extent (the test part is separate) but not yet this year, I am afraid! The course is completed in about six weeks, implying the students have to work real hard between classes, and to ensure this, they must hand back solved problems from the chapter(s) covered in the previous class at the beginning of the next class.

Happy B’day, ‘Og!

This blog started a year ago with the definitely poor prediction that “I will most likely not update it fairly often”… I have been spending an increasing amount of time on the ‘Og, in reply to an increasing number of connections, and I am not sure this is an efficient strategy, but I do like this media as a way to immediately discuss about read papers and tech’ reports. (I wish journals like Bayesian Analysis would allow for a bloggin’ section, even though I understand this is a severe commitment because of moderation issues.) As pointed by Andrew Gelman, bloggin’ is dangerously addictive! Here’s, by popular demand, the top of the hits over the past year:

Title	Views
Of black swans and bleak prospects	898
Tornado in Central Park	864
Bayes’ Theorem	595
ABC in Paris, June 26	383
About	306
Sequential Monte Carlo without likelihood	279
Reference prior for logistic regression	257
Bayesian p-values	229
Anomalies in the Iranian election	212

Interestingly, and reassuringly!, besides both first entries that address highly popular topics, the other hits are about statistical topics! And the list includes Bayes’ Theorem, ABC and SMC.

New typos in Monte Carlo Statistical Methods

Three weeks ago, I got this email from Amir Alipour, an Iranian student, about typos in Monte Carlo Statistical Method:

“I found some typos in the book which were not reported at your website. I list them blow, I would appreciate if you let me know if I`m right.
1.       Page 4, line 9,  , the index should not be instead of ?
2.       Page 4, example 1.3, last line, , should be (as we have ).
3.       Page 5, the likelihood of MA(q), it seems should  change to  .
4.       Page 8, formula (1.10).  The gradient symbol is used for the first time without introducing, while it is used for the second time on page 19 with introducing.
5.       Page 8, Example 1.6, the log part in , should  change to .
6.       Page 10, in modified Bessel function, should change to .
7.       Page 10, Example 1.9, in the likelihood function, the power of should be , and the power of the function under product should be . (Even Figure 1.1 is not consistent with likelihood)”

and I have posted those new typos on the associated webpage. Amir Alipour has thus managed to find seven yet undiscovered typos in the first ten pages of the book! I am quite grateful to Amir Alipour for signaling those typos. Especially the final one which is due to an intented presentation of the density as a polynomial, with a poor wording: the likelihood of a sample is proportional to a power of a polynomial in the location parameter. (And there still is a typo since should be …) Now I can only hope Amir Alipour can proceed through the whole book with the same amount of dedication!

Spook Country

“Say,” he said to Brown who was looking at his phone as if he wished he knew a way to torture it, “this NSA data-mining thing…”

When I attended MaxEnt 2009 in Oxford, I bought William Gibson‘s Spook Country at the university bookstore as it was on sale for $5… I have read it during the past week, finishing it this morning in the 5:30 bus to Helsinki airport, and I am quite disappointed. (Incidentally, I visited yesterday the Akateeminen Kirjakauppa bookstore in Helsinki and found there an incredibly well-provided fantasy section—in English—that beats by far the major chains in England!) I love Gibson‘s early cyber-punk books and I can still remember the excitement of reading Neuromancer for the first time, while I was completing my thesis.

“We have been buying into data mining at Blue Ant.”

The style was very innovative, sharp and tense, with this then-novel use of existing brands to shorten the descriptions, and the story was gripping, with insights of what would become the cyberspace. Even the later Virtual Light had fascinating findings, like its delivery cyclist and its recycling of the Golden Gate Bridge into a squatter community.

“What does Chombo…do?” “It implements finite difference methods for the solution of partial differential equations, on block structured, adaptively refined rectangular grids.”

In my opinion, Spook Country is over-exploiting the same stylistic lines as those earlier books with very short chapters, an abundance of brands (Apple at the forefront!), a central role of technology and virtual reality, and three characterial threads interweaved. However, the story does not click in. There are too many improbable coincidences and the characters are definitely caricatural, while reminding me of the previous books: the female artist drawn into investigation for lack of money, the geek computer genius, the woodoo inspired ninja-like thug, the tough CIA spook, the media executive with unlimited wealth… Without going into spoilers, the plot is fairly thin, with those three different groups chasing after the same container, and obviously ending up together. The technological inventivity of the previous novels has disappeared as well—the above quote about Chombo is taken verbatim from the Berkeley Lab website!—, which may explain why William Gibson does not intend to continue writing sci’-fi’ novels.