## ABC in Helsinki [on-board]

Posted in pictures, Statistics, Travel, University life with tags , , , , , , , , , , , , , , on May 17, 2016 by xi'an

ABC in Helsinki (a.k.a. ABCruise) has started! With a terrific weather most adequate for a cruise on the Baltic. The ship on which the workshop takes place is certainly larger than any I have been on, including the Channel ferries, and the inside alley looks rather like a shopping centre! However, the setting is exceptional, with comfy sea-facing cabins and pleasant breaks (including fancy tea!) Plus,  we have a quiet and cosy conference room that makes one forgets one is on a boat. Until it starts rocking. Or listing! The cruise boat is definitely large enough to be fairly stable. A unique experience we could consider for future (AB-see) workshops (with the caveat that we benefited from exceptional circumstances that brought the costs down to ridiculous amounts).

Richard Everitt talked about the synthetic likelihood approach and its connection with ABC. Making clear for me a point I had somewhat forgotten, namely that the approximative likelihood is a Gaussian at the observed summary statistics, but one centred at empirical moments derived from the simulation of pseudo summaries based on a given value of the parameter θ. So it is not an exact approach in that it does not converge to the true likelihood as the number of simulation grows to infinity. (While a kernel would converge.) That means it may (will) misrepresent the tails unless the distribution of the summary statistic is close to Normal. Richard also introduced bootstrap or bags of little bootstraps in order to speed up the generation of the pseudo-data, which makes sense albeit it moves the sampling away from the true model since it is conditional on  a single simulation.

Jean-Michel Marin introduced the ABC inference algorithm we are currently working on, using regression random forests that differ from the classification forests we used for model selection. (The paper is close to completion so I hope to be able to tell more in a near future!) Clara Grazian presented her semi-parametric work using ABC with Brunero Liseo. That was part of her thesis. Thomas Schön presented an extension of his particle Gibbs with adaptive sampling to the case of degenerate transitions, using an ABC approximation to get around this central problem. A very interesting entry that I need to study deeper. And Caroline Colijn talked about ABC for trees, mostly about the selection of summary statistics towards comparing tree topologies, with  a specific distance between trees that caters to the topology and only the topology.

## ritorno da Roma

Posted in pictures, Travel, University life with tags , , , , , , , on April 24, 2016 by xi'an

## a day in Roma

Posted in Books, pictures, Running, Statistics, Travel, University life, Wines with tags , , , , , on April 18, 2016 by xi'an

Last Friday I spent about 24 hours in Roma due to Clara Grazian defending her thesis there, which was awarded the highest PhD degree from both Sapienza Università di Roma and Université Paris-Dauphine. Her thesis was composed of her papers on ABC for integrated likelihood, on Jeffreys priors for mixtures (which sadly was rejected a few weeks ago), and on scoring rules à la Dawid for model choice. Clara was the first student to graduate from the joint graduate program between Sapienza and Paris-Dauphine, and I look forward the graduation of the next students!It was absolutely wonderful to be there, not only to attend the defence with Marilena Barbieri, Fabrizio Leisen, and Brunero Liseo (who was also Clara’s supervisor) and to congratulate Clara on the completion of her thesis, but also to meet [albeit much too briefly] with old friends, to enjoy great Roman food, perfect weather, my usual long run along the Tiber and twelve of its bridges in the glorious Roman morning, and “just” this unique feeling of Roma in Spring…

## morning run in Roma

Posted in pictures, Running, Travel, University life with tags , , , , , on April 15, 2016 by xi'an

## no country for odd means

Posted in Books, Kids, Statistics, University life with tags , , , , , , on November 16, 2015 by xi'an

This morning, Clara Grazian and I arXived a paper about Jeffreys priors for mixtures. This is a part of Clara’s PhD dissertation between Roma and Paris, on which she has worked for the past year. Jeffreys priors cannot be computed analytically for mixtures, which is such a drag that it led us to devise the delayed acceptance algorithm. However, the main message from this detailed study of Jeffreys priors is that they mostly do not work for Gaussian mixture models, in that the posterior is almost invariably improper! This is a definite death knell for Jeffreys priors in this setting, meaning that alternative reference priors, like the one we advocated with Kerrie Mengersen and Mike Titterington, or the similar solution in Roeder and Wasserman, have to be used. [Disclaimer: the title has little to do with the paper, except that posterior means are off for mixtures…]

## ABC for copula estimation

Posted in Books, Kids, pictures, Statistics, Travel, University life with tags , , , , , , , on March 23, 2015 by xi'an

Clara Grazian and Brunero Liseo (di Roma) have just arXived a note on a method merging copulas, ABC, and empirical likelihood. The approach is rather hybrid and thus not completely Bayesian, but this must be seen as a consequence of an ill-posed problem. Indeed, as in many econometric models, the model there is not fully defined: the marginals of iid observations are represented as being from well-known parametric families (and are thus well-estimated by Bayesian tools), while the joint distribution remains uncertain and hence so does the associated copula. The approach in the paper is to proceed stepwise, i.e., to estimate correctly each marginal, well correctly enough to transform the data by an estimated cdf, and then only to estimate the copula or some aspect of it based on this transformed data. Like Spearman’s ρ. For which an empirical likelihood is computed and aggregated to a prior to make a BCel weight. (If this sounds unclear, each BEel evaluation is based on a random draw from the posterior samples, which transfers some uncertainty in the parameter evaluation into the copula domain. Thanks to Brunero and Clara for clarifying this point for me!)

At this stage of the note, there are two illustrations revolving around Spearman’s ρ. One on simulated data, with better performances than a nonparametric frequentist solution. And another one on a Garch (1,1) model for two financial time-series.

I am quite glad to see an application of our BCel approach in another domain although I feel a tiny bit uncertain about the degree of arbitrariness in the approach, from the estimated cdf transforms of the marginals to the choice of the moment equations identifying the parameter of interest like Spearman’s ρ. Especially if one uses a parametric copula which moments are equally well-known. While I see the practical gain in analysing each component separately, the object created by the estimated cdf transforms may have a very different correlation structure from the true cdf transforms. Maybe there exist consistency conditions on the estimated cdfs… Maybe other notions of orthogonality or independence could be brought into the picture to validate further the two-step solution…

## Gagliotto, Sangiovese di Romagna (superiore!)

Posted in pictures, Wines with tags , , , on September 20, 2014 by xi'an