When has Bayesian analysis really made a difference???

With Kerrie Mengersen (QUT, Brisbane), we are launching a call for Bayesian “stories”, towards a collective paper/a special issue:

When has Bayesian analysis really made a difference?

Following the publication of “the theory that would not die” by Sharon McGrayne, about how Bayesian analysis contributed to science and the World in general, we [Kerrie Mengersen (QUT, Brisbane) and Christian Robert (Paris-Dauphine)] would like to put together a collection of six-page vignettes that describe real cases in which Bayesian analysis has been the only way to crack a really important problem.
To this end, we are launching a call for one page proposals that address the following questions.

• What was the big problem to be solved? We mean big.
• Why was it so difficult to solve statistically?
• What was the Bayesian resolution?
• Why couldn’t it be solved by other means? What were the shortcomings of other statistical solutions?
• What was the overall impact of this Bayesian analysis on the real world?

We will then review those proposals and select the most significant ones towards the production of six page vignettes, aiming them to be published in a special issue or a multiple authored paper of a mainstream statistical journal. The deadline for the submission of a one-page proposal is September 30. It should be sent to Christian P. Robert at bayesianstatistics@gmailcom in pdf format. The final deadline will depend on the journal editor.

Obviously, if you happen to be like me at JSM 2011 this week and have a proposal (or journal!) in mind, feel free to talk to me about this! (I have also been waiting ages for a copy—two, actually—of the theory that would not die towards the dual goals of reading it and writing a review, but both channels failed to deliver.)

Questions on ABC

Our ABC survey for Statistics and Computing (and the ABC special issue!) has been quickly revised, resubmitted, and rearXived. Here is our conclusion about some issues that remain unsolved (much more limited in scope than the program drafted by Halton!):

1. the convergence results obtained so far are unpractical in that they require either the tolerance to go to zero or the sample size to go to infinity. Obtaining exact error bounds for positive tolerances and finite sample sizes would bring a strong improvement in both the implementation of the method and in the assessment of its worth.
2. in particular, the choice of the tolerance is so far handled from a very empirical perspective. Recent theoretical assessments show that a balance between Monte Carlo variability and target approximation is necessary, but the right amount of balance must be reached towards a practical implementation.
3.  even though ABC is often presented as a converging method that approximates Bayesian inference, it can also be perceived as an inference technique per se and hence analysed in its own right. Connections with indirect inference have already been drawn, however the fine asymptotics of ABC would be most useful to derive. Moreover, it could indirectly provide indications about the optimal calibration of the algorithm.
4. in connection with the above, the connection of ABC-based inference with other approximative methods like variational Bayes inference is so far unexplored. Comparing and interbreeding those different methods should become a research focus as well.
5. the construction and selection of the summary statistics is so far highly empirical. An automated approach based on the principles of data analysis and approximate sufficiency would be much more attractive and convincing, especially in non-standard and complex settings. \item the debate about ABC-based model choice is so far inconclusive in that we cannot guarantee the validity of the approximation, while considering that a “large enough” collection of summary statistics provides an acceptable level of approximation. Evaluating the discrepancy by exploratory methods like the bootstrap would shed a much more satisfactory light on this issue.
6.  the method necessarily faces limitations imposed by large datasets or complex models, in that simulating pseudo-data may itself become an impossible task. Dimension-reducing techniques that would simulate directly the summary statistics will soon become necessary.

Statistics and Computing and ABC

Statistics and Computing has received several papers on ABC and plans to make a special ABC issue out of these. All submissions related to ABC that are made prior to late June 2011 and that are accepted will be published in this special issue. The special issue is identified as a specific article type on the on-line submissions page.

In case you have questions or requests about this special issue, please directly contact the Editor Gilles Celeux or the publishing editor. Not me! I am simply forwarding the announcement from the Editor to all those interested.