Archive for likelihood-free methods

likelihood-free and summary-free?

Posted in Books, Mountains, pictures, Statistics, Travel with tags , , , , , , , , , , , , , on March 30, 2021 by xi'an

My friends and coauthors Chris Drovandi and David Frazier have recently arXived a paper entitled A comparison of likelihood-free methods with and without summary statistics. In which they indeed compare these two perspectives on approximate Bayesian methods like ABC and Bayesian synthetic likelihoods.

“A criticism of summary statistic based approaches is that their choice is often ad hoc and there will generally be an  inherent loss of information.”

In ABC methods, the recourse to a summary statistic is often advocated as a “necessary evil” against the greater evil of the curse of dimension, paradoxically providing a faster convergence of the ABC approximation (Fearnhead & Liu, 2018). The authors propose a somewhat generic selection of summary statistics based on [my undergrad mentors!] Gouriéroux’s and Monfort’s indirect inference, using a mixture of Gaussians as their auxiliary model. Summary-free solutions, as in our Wasserstein papers, rely on distances between distributions, hence are functional distances, that can be seen as dimension-free as well (or criticised as infinite dimensional). Chris and David consider energy distances (which sound very much like standard distances, except for averaging over all permutations), maximum mean discrepancy as in Gretton et al. (2012), Cramèr-von Mises distances, and Kullback-Leibler divergences estimated via one-nearest-neighbour formulas, for a univariate sample. I am not aware of any degree of theoretical exploration of these functional approaches towards the precise speed of convergence of the ABC approximation…

“We found that at least one of the full data approaches was competitive with or outperforms ABC with summary statistics across all examples.”

The main part of the paper, besides a survey of the existing solutions, is to compare the performances of these over a few chosen (univariate) examples, with the exact posterior as the golden standard. In the g & k model, the Pima Indian benchmark of ABC studies!, Cramèr does somewhat better. While it does much worse in an M/G/1 example (where Wasserstein does better, and similarly for a stereological extremes example of Bortot et al., 2007). An ordering inversed again for a toad movement model I had not seen before. While the usual provision applies, namely that this is a simulation study on unidimensional data and a small number of parameters, the design of the four comparison experiments is very careful, eliminating versions that are either too costly or too divergence, although this could be potentially criticised for being unrealistic (i.e., when the true posterior is unknown). The computing time is roughly the same across methods, which essentially remove the call to kernel based approximations of the likelihood. Another point of interest is that the distance methods are significantly impacted by transforms on the data, which should not be so for intrinsic distances! Demonstrating the distances are not intrinsic…

PhD position for research in ABC in Chalmers University

Posted in Statistics with tags , , , , , , , , , on May 27, 2020 by xi'an

[Posting a call for PhD candidates from Umberto Piccini as the deadline is June 1, next Monday!]

A PhD student position in mathematical statistics on simulation-based inference methods for models with an “intractable” likelihood is available at the Dept. Mathematical Sciences, Chalmers University, Gothenburg (Sweden).

You will be part of an international collaboration to create new methodology bridging between simulation-based inference (such as approximate Bayesian computation and other likelihood-free methods) and deep neuronal networks. The goal is to ease inference for stochastic modelling.

Details on the project and the essential requirements are at https://www.chalmers.se/en/departments/math/research/research-groups/AIMS/Pages/ai-project-5.aspx

The PhD student position is fully funded and is up to 5 years, in the dynamic and international city of Gothenburg, the second largest city in Sweden, https://www.goteborg.com/en/ As a PhD student in Mathematical Sciences you will have opportunities for many inspiring conversations, a lot of autonomous work and some travel.

The position will be supervised by Assoc. Prof. Umberto Picchini.

Apply by 01 June 2020 following the instructions at
https://www.chalmers.se/en/about-chalmers/Working-at-Chalmers/Vacancies/Pages/default.aspx?rmpage=job&rmjob=8556

For informal enquiries, please get in touch with Umberto Picchini

another mirror of ABC in Gre[e]noble

Posted in Statistics with tags , , , , , , , , , , on March 3, 2020 by xi'an

There will now be a second mirror workshop of ABC in Grenoble. Taking place at the Université de Montpellier, more precisely at the Alexander Grothendieck Montpellier Institute, Building 9, room 430 (4th floor), Triolet Campus. It is organised by my friend Jean-Michel Marin. Great to see a mirror at one of the major breeding places of ABC, where I personally heard of ABC for the first time and met several of the main A[B]Ctors..! The dates are 19-20 March, with talks transmitted from 9am to 5am [GMT+1]. Since the video connection can accommodate 1918 more mirrors, if anyone else is interested in organising another mirror, please contact me for technical details.

in Bristol for the day

Posted in pictures, Statistics, Travel, University life with tags , , , , , , , , , , , on February 28, 2020 by xi'an

I am in Bristol for the day, giving a seminar at the Department of Statistics where I had not been for quite a while (and not since the Department has moved to a beautifully renovated building). The talk is on ABC-Gibbs, whose revision is on the verge of being resubmitted. (I also hope Greta will let me board my plane tonight…)

mirror of ABC in Grenoble

Posted in pictures, Statistics, Travel, University life with tags , , , , , , , on February 26, 2020 by xi'an

I am quite glad to announce that there will definitely be at least one mirror workshop of ABC in Grenoble. Taking place at Warwick University, in the Zeeman building (room MS0.05) and organised by my colleague Rito Dutta. The dates are 19-20 March, with talks transmitted from 9am to 5am [GMT+1]. Since the video connection can accommodate 19 more mirrors, if anyone is interested in organising an other mirror, please contact me for technical details.

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