Jeff Rosenthal is the AMSI-SSA (Australia Mathematical Sciences Institute – Statistical Society of Australia) lecturer this year and, as I did in 2012, will tour Australia giving seminars. Including this one at QUT. Enjoy, if you happen to be down-under!
Archive for Australia
“This formulation reveals an interesting connection between multiple hypothesis testing and mixture modelling with the class labels corresponding to the accepted hypotheses in each test.”
After my seminar at Monash University last Friday, David Dowe pointed out to me the recent work by Enes Makalic and Daniel Schmidt on minimum description length (MDL) methods for multiple testing as somewhat related to our testing by mixture paper. Work which appeared in the proceedings of the 4th Workshop on Information Theoretic Methods in Science and Engineering (WITMSE-11), that took place in Helsinki, Finland, in 2011. Minimal encoding length approaches lead to choosing the model that enjoys the smallest coding length. Connected with, e.g., Rissannen‘s approach. The extension in this paper consists in considering K hypotheses at once on a collection of m datasets (the multiple then bears on the datasets rather than on the hypotheses). And to associate an hypothesis index to each dataset. When the objective function is the sum of (generalised) penalised likelihoods [as in BIC], it leads to selecting the “minimal length” model for each dataset. But the authors introduce weights or probabilities for each of the K hypotheses, which indeed then amounts to a mixture-like representation on the exponentiated codelengths. Which estimation by optimal coding was first proposed by Chris Wallace in his book. This approach eliminates the model parameters at an earlier stage, e.g. by maximum likelihood estimation, to return a quantity that only depends on the model index and the data. In fine, the purpose of the method differs from ours in that the former aims at identifying an appropriate hypothesis for each group of observations, rather than ranking those hypotheses for the entire dataset by considering the posterior distribution of the weights in the later. The mixture has somehow more of a substance in the first case, where separating the datasets into groups is part of the inference.
Taking advantage of being in San Francisco, I flew yesterday to Australia over the Pacific, crossing for the first time the day line. The 15 hour Qantas flight to Sydney was remarkably smooth and quiet, with most passengers sleeping for most of the way, and it gave me a great opportunity to go over several papers I wanted to read and review. Over the next week or so, I will work with my friends and co-authors David Frazier and Gael Martin at Monash University (and undoubtedly enjoy the great food and wine scene!). Before flying back to Paris (alas via San Francisco rather than direct).
Bayes on the Beach is a yearly conference taking place in Queensland Gold Coast and organised by Kerrie Mengersen and her BRAG research group at QUT. To quote from the email I just received, the conference will be held at the Mantra Legends Hotel on Surfers Paradise, Gold Coast during November 7 – 9, 2016. The conference provides a forum for discussion on developments and applications of Bayesian statistics, and includes keynote presentations, tutorials, practical problem-based workshops, invited oral presentations, and poster presentations. Abstract submissions are now open until September 2.
With David Frazier and Gael Martin from Monash University, and with Judith Rousseau (Paris-Dauphine), we have now completed and arXived a paper entitled Asymptotic Properties of Approximate Bayesian Computation. This paper undertakes a fairly complete study of the large sample properties of ABC under weak regularity conditions. We produce therein sufficient conditions for posterior concentration, asymptotic normality of the ABC posterior estimate, and asymptotic normality of the ABC posterior mean. Moreover, those (theoretical) results are of significant import for practitioners of ABC as they pertain to the choice of tolerance ε used within ABC for selecting parameter draws. In particular, they [the results] contradict the conventional ABC wisdom that this tolerance should always be taken as small as the computing budget allows.
Now, this paper bears some similarities with our earlier paper on the consistency of ABC, written with David and Gael. As it happens, the paper was rejected after submission and I then discussed it in an internal seminar in Paris-Dauphine, with Judith taking part in the discussion and quickly suggesting some alternative approach that is now central to the current paper. The previous version analysed Bayesian consistency of ABC under specific uniformity conditions on the summary statistics used within ABC. But conditions for consistency are now much weaker conditions than earlier, thanks to Judith’s input!
- Li and Fearnhead (2015) considers an ABC algorithm based on kernel smoothing, whereas our interest is the original ABC accept-reject and its many derivatives
- our theoretical approach permits a complete study of the asymptotic properties of ABC, posterior concentration, asymptotic normality of ABC posteriors, and asymptotic normality of the ABC posterior mean, whereas Li and Fearnhead (2015) is only concerned with asymptotic normality of the ABC posterior mean estimator (and various related point estimators);
- the results of Li and Fearnhead (2015) are derived under very strict uniformity and continuity/differentiability conditions, which bear a strong resemblance to those conditions in Yuan and Clark (2004) and Creel et al. (2015), while the result herein do not rely on such conditions and only assume very weak regularity conditions on the summaries statistics themselves; this difference allows us to characterise the behaviour of ABC in situations not covered by the approach taken in Li and Fearnhead (2015);