Archive for ABC convergence

asymptotic properties of ABC now appeared

Posted in Books, Statistics, University life with tags , , , , , , on September 1, 2018 by xi'an

Our paper with David Frazier, Gael Martin and Judith Rousseau has appeared in print in Biometrika, Volume 105, Issue 3, 1 September 2018, Pages 593–607, almost exactly two years after it was submitted. I am quite glad with the final version, though, and grateful for the editorial input, as the paper clearly characterises the connection between the tolerance level ε and the convergence rate of the summary statistic to its parameter identifying asymptotic mean. Asymptotic in the sample size, that is.

ABC’ptotics on-line

Posted in Statistics with tags , , , , , , , on June 14, 2018 by xi'an

Our paper on Asymptotic properties of ABC with David Frazier, Gael Martin, and Judith Rousseau, is now on-line on the Biometrika webpage. Coincidentally both papers by Wentao Li and Paul Fearnhead on ABC’ptotics are published in the June issue of the journal.

Approximate Bayesian computation allows for statistical analysis using models with intractable likelihoods. In this paper we consider the asymptotic behaviour of the posterior distribution obtained by this method. We give general results on the rate at which the posterior distribution concentrates on sets containing the true parameter, the limiting shape of the posterior distribution, and the asymptotic distribution of the posterior mean. These results hold under given rates for the tolerance used within the method, mild regularity conditions on the summary statistics, and a condition linked to identification of the true parameters. Implications for practitioners are discussed.

back to Wales [54th Gregynog Statistical Conference]

Posted in Mountains, pictures, Running, Travel, University life with tags , , , , , , , , on March 23, 2018 by xi'an

Today, provided the Air France strike let me fly to Birmingham airport!, I am back at Gregynog Hall, Wales, for the weekend conference organised there every year by some Welsh and English statistics departments, including Warwick. Looking forward to the relaxed gathering in the glorious Welsh countryside (and hoping that my knee will have sufficiently recovered for some trail running around Gregynog Hall…!) Here are the slides of the talk I will present tomorrow:

impressions from EcoSta2017 [guest post]

Posted in pictures, Statistics, Travel, University life with tags , , , , , , , , , on July 6, 2017 by xi'an

[This is a guest post on the recent EcoSta2017 (Econometrics and Statistics) conference in Hong Kong, contributed by Chris Drovandi from QUT, Brisbane.]

There were (at least) two sessions on Bayesian Computation at the recent EcoSta (Econometrics and Statistics) 2017 conference in Hong Kong. Below is my review of them. My overall impression of the conference is that there were lots of interesting talks, albeit a lot in financial time series, not my area. Even so I managed to pick up a few ideas/concepts that could be useful in my research. One criticism I had was that there were too many sessions in parallel, which made choosing quite difficult and some sessions very poorly attended. Another criticism of many participants I spoke to was that the location of the conference was relatively far from the city area.

In the first session (chaired by Robert Kohn), Minh-Ngoc Tran spoke about this paper on Bayesian estimation of high-dimensional Copula models with mixed discrete/continuous margins. Copula models with all continuous margins are relatively easy to deal with, but when the margins are discrete or mixed there are issues with computing the likelihood. The main idea of the paper is to re-write the intractable likelihood as an integral over a hypercube of ≤J dimensions (where J is the number of variables), which can then be estimated unbiasedly (with variance reduction by using randomised quasi-MC numbers). The paper develops advanced (correlated) pseudo-marginal and variational Bayes methods for inference.

In the following talk, Chris Carter spoke about different types of pseudo-marginal methods, particle marginal Metropolis-Hastings and particle Gibbs for state space models. Chris suggests that a combination of these methods into a single algorithm can further improve mixing. Continue reading

talk at Trinity College

Posted in pictures, Statistics, Travel, University life with tags , , , , , , , on May 7, 2017 by xi'an

Tomorrow noon, I will give a talk at Trinity College Dublin on the asymptotic properties of ABC. (Here are the slides from the talk I gave in Berlin last month.)

CORE talk at Louvain-la-Neuve

Posted in Statistics with tags , , , , , , , on March 16, 2017 by xi'an

Tomorrow, I will give a talk at the seminar for econometrics and finance of CORE, in Louvain-la-Neuve, Belgium. Here are my slides, recycled from several earlier talks and from Judith’s slides in Banff:

 

ABC’ory in Banff [17w5025]

Posted in Mountains, pictures, Statistics, Travel, University life with tags , , , , , , , , , on February 23, 2017 by xi'an

Cascade mountain, Banff, March 18, 2012Another great day of talks and discussions at BIRS! Continuing on the themes of the workshop between delving into the further validation of those approximation techniques and the devising of ever more approximate solutions for ever more complex problems. Among the points that came clearer to me through discussion, a realisation that the synthetic likelihood perspective is not that far away from our assumptions in the consistency paper. And that a logistic version of the approach can be constructed as well. A notion I had not met before (or have forgotten I had met) is the one of early rejection ABC, which should actually be investigated more thoroughly as it should bring considerable improvement in computing time (with the caveats of calibrating the acceptance step before producing the learning sample and of characterising the output).  Both Jukka Corander and Ewan Cameron reminded us of the case of models that take minutes or hours to produce one single dataset. (In his talk on some challenging applications, Jukka Corander chose to move from socks to boots!) And Jean-Michel Marin produced an illuminating if sobering experiment on the lack of proper Bayesian coverage by ABC solutions. (It appears that Ewan’s video includes a long empty moment when we went out for the traditional group photo, missing the end of his talk.)