ABC with empirical likelihood (second round)

We (Kerrie Mengersen, Pierre Pudlo, and myself) have now revised our ABC with empirical likelihood paper and resubmitted both to arXiv and to PNAS as “Approximate Bayesian computation via empirical likelihood“. The main issue raised by the referees was that the potential use of the empirical likelihood (EL) approximation is much less widespread than the possibility of simulating pseudo-data, because EL essentially relies on an iid sample structure, plus the availability of parameter defining moments. This is indeed the case to some extent and also the reason why we used a compound likelihood for our population genetic model. There are in fact many instances where we simply cannot come up with a regular EL approximation… However, the range of applications of straight EL remains wide enough to be of interest, as it includes most dynamical models like hidden Markov models. To illustrate this point further, we added (in this revision) an example borrowed from the recent Biometrika paper by David Cox and Christiana Kartsonaki (which proposes a frequentist alternative to ABC based on fractional design). This model ended up being fairly appealing wrt our perspective: while the observed data is dependent in a convoluted way, being a superposition of N renewal processes with gamma waiting times, it is possible to recover an iid structure at the same cost as a regular ABC algorithm by using the pseudo-data to recover an iid process (the sequence of renewal processes indicators)…The outcome is quite favourable to ABCel in this particular case, as shown by the graph below (top: ABCel, bottom: ABC, red line:truth):

This revision (started while visiting Kerrie in Brisbane) was thus quite beneficial to our perception of ABC in that (a) it is indeed not as universal as regular ABC and this restriction should be spelled out (the advantage being that, when it can be implemented, it usually runs much much faster!), and (b) in cases where the pseudo-data must be simulated, EL provides a reference/benchmark for the ABC output that comes for free… Now I hope to manage to get soon out of the “initial quality check” barrage to reach the Editorial Board!

back from down under

After a sunny weekend to unpack and unwind, I am now back to my normal schedule, on my way to Paris-Dauphine for an R (second-chance) exam. Except for confusing my turn signal for my wiper, thanks to two weeks of intensive driving in four Australian states!, things are thus back to “normal”, meaning that I have enough of a control of my time to handle both daily chores like the R exam and long-term projects. Including the special issues of Statistical Science, TOMACS, and CHANCE (reviewing all books of George Casella in memoriam). And the organisation of MCMSki 4, definitely taking place in Chamonix on January 6-8, 2014, hopefully under the sponsorship of the newly created BayesComp section of ISBA. And enough broadband to check my usual sites and to blog ad nauseam.

This trip to Australia, along the AMSI Lectures as well as the longer visits to Monash and QUT, has been quite an exciting time, with many people met and ideas discussed. I came back with a (highly positive) impression of Australian universities as very active places, just along my impression of Australia being a very dynamic and thriving country, far far away from the European recession. I was particularly impressed by the number of students within Kerrie Mengersen’s BRAG group, when we did held discussions in classrooms that felt full like a regular undergrad class! Those discussions and meetings set me towards a few new projects along the themes of mixture estimation and model choice, as well as convergence assessment. During this trip, I however also felt the lack of long “free times” I have gotten used to, thanks to the IUF chair support, where I can pursue a given problem for a few hours without interruption. Which means that I did not work as much as I wanted to during this tour and will certainly avoid such multiple-step trips in a near future. Nonetheless, overall, the own under” experience was quite worth it! (Even without considering the two weeks of vacations I squeezed in the middle.)

Back to “normal” also means I already had two long delays caused by suicides on my train line…

non-randomness

A question sent by Eric, who attended my Public Lecture last week in Brisbane:

Last year at this time, Peter Sarnak toured Australia talking about randomness in number theory and Moebius randomness in dynamics. Recently,  he pointed a paper on the arXiv in which he claims that the distribution of [integer coordinate] points on the sphere of radius √n which satisfy

is random as n goes to infinity (the paper is much more precise).  You mentioned tests which look for non-randomness.  How does one test for a non-random distribution of points on the sphere?

Interesting question, both for linking two AMSI Lecture tours (Peter Sarnak’s schedule sounded more gruelling than mine!) and for letting me get a look at this paper. Plus for the connection with probabilistic number theory. This paper indeed stands within the area of randomness in number theory rather than random generation and I do not see an obvious connection here, but the authors of the paper undertake a study of the randomness of the solutions to the above equation for a fixed n using statistics and their limiting distribution. (I am not certain of the way points are obtained over a square on Fig. 1, presumably this is using the spherical coordinates of the projections over the unit sphere in R³.) Their statistics are the electrostatic energy, Ripley’s point pair statistic, the nearest neighbour spacing measure, minimum spacing, and the covering radius. The most surprising feature of this study is that this randomness seems to be specific to the dimension 3 case: when increasing the number of terms in the above equation, the distribution of the solutions seems more rigid and less random…

AMSI-SSAI Lectures #4-5

Yesterday night I gave my AMSI-SSAI public lecture on simulation at the University of Melbourne. Following a seminar in the early afternoon on ABC (essentially the same as in Adelaide and UWS, although I should shorten it). The seminar was well-attended, despite being during the first week of the semester and between classes. I am afraid the lecture did not draw many members of the public, though, which is not a great surprise given my esoteric (?) title, and I am afraid the academics who attended the talk did not really need this basic intro to simulations… I also visited the offices of AMSI on the campus, where I was very warmly welcomed, thank you! This even included an interview with a media officer who happened to be a Physics Honour student at the University of Melbourne, working on a cool radar data analysis. (This Honour program is an interesting entry into research that is missing in the French curriculum, providing students interested in research to spend a year mostly working on a research project right after undergraduate graduation…) In addition, it was an opportunity to look at the great posters made by AMSI to promote math in high schools with the motto “maths make your career count“. Today, I give a seminar at Monash on ABC model choice.

simulation, a ubiquitous tool

After struggling for quite a while on that AMSI public lecture talk, and dreading its loss with the problematic Macbook, I managed to complete a first draft last night in Adelaide, downloading [at high financial cost!] a final set of images from the Web (plus a few personal ones, like a picture of my son’s Warhammer figurines!). Having very few inklings about the level and the expectations of the audience (if any!), I cannot say if this introduction to simulation is too basic. I will see after the first talk whether or not the aim was off-target… In any case, I am glad I was forced into writing this talk as I had always wanted to have a general-audience introduction to simulation at the ready and can now recycle it easily when and if needed. I will certainly use it in my R class this semester.