**T**his week, I gave a short and introductory course in Warwick for the CDT (PhD) students on my perceived connections between reverse logistic regression à la Geyer and GANS, among other things. The first attempt was cancelled in 2020 due to the pandemic, the second one in 2021 was on-line and thus offered little possibilities for interactions. Preparing for this third attempt made me read more papers on some statistical analyses of GANs and WGANs, which was more satisfactory [for me] even though I could not get into the technical details…

## Archive for ABC

## Recent Advances in Approximate Bayesian Inference [YSE, 15.2.22]

Posted in Statistics, University life with tags ABC, Approximate Bayesian computation, approximate Bayesian inference, Bernoulli society, PMCABC, webinar on May 11, 2022 by xi'an

**O**n June 15, the Young Statisticians Europe initiative is organising an on-line seminar on approximate Bayesian inference. With talks by

- Lorenzo Pacchiardi, University of Oxford, United Kingdom
- Emilia Pompe, University of Oxford, United Kingdom
- Łukasz Rajkowski, University of Warsaw, Poland
- Théo Moins, Inria Grenoble Rhône-Alpes, France

starting at 7:00 PT / 10:00 EST / 16:00 CET. The registration form is available here.

## Concentration and robustness of discrepancy-based ABC [One World ABC ‘minar, 28 April]

Posted in Statistics, University life with tags ABC, Approximate Bayesian computation, approximate Bayesian inference, discrepancy, Japan, One World ABC Seminar, RIKEN, sufficiency, Tokyo, University of Warwick, Wasserstein distance, webinar on April 15, 2022 by xi'an**O**ur next speaker at the One World ABC Seminar will be Pierre Alquier, who will talk about “

*Concentration and robustness of discrepancy-based ABC*“, on

**Thursday April 28, at 9.30am UK time,**with an abstract reported below.

Approximate Bayesian Computation (ABC) typically employs summary statistics to measure the discrepancy among the observed data and the synthetic data generated from each proposed value of the parameter of interest. However, finding good summary statistics (that are close to sufficiency) is non-trivial for most of the models for which ABC is needed. In this paper, we investigate the properties of ABC based on integral probability semi-metrics, including MMD and Wasserstein distances. We exhibit conditions ensuring the contraction of the approximate posterior. Moreover, we prove that MMD with an adequate kernel leads to very strong robustness properties.

## likelihood-free nested sampling

Posted in Books, Statistics with tags ABC, ABC-SMC, Approximate Bayesian computation, nested sampling, particle filter, PLoS computational biology, pMCMC on April 11, 2022 by xi'an**L**ast week, I came by chance across a paper by Jan Mikelson and Mustafa Khammash on a likelihood-free version of nested sampling (a popular keyword on the ‘Og!). Published in 2020 in PLoS Comput Biol. The setup is a parameterised and hidden state-space model, which allows for an approximation of the (observed) likelihood function L(θ|y) by means of a particle filter. An immediate issue with this proposal is that a *novel *filter need be produced for a *new* value of the parameter θ, which makes it enormously expensive. It then gets more bizarre as the [Monte Carlo] distribution of the particle filter approximation ô(θ|y) is agglomerated with the original prior π(θ) as a joint “prior” [despite depending on the observed y] and a nested sampling is conducted with level sets of the form

ô(θ|y)>ε.

Actually, if the Monte Carlo error was null, that is, if the number of particles was infinite,

ô(θ|y)=L(θ|y)

implies that this is indeed the original nested sampler. Simulation from the restricted region is done by constructing an extra density estimator of the constrained distribution (in θ)…

“We have shown how using a Monte Carlo estimate over the livepoints not only results in an unbiased estimator of the Bayesian evidence Z, but also allows usto derive a formulation for a lower bound on the achievable variance in each iteration (…)”

As shown by the above the authors insist on the unbiasedness of the particle approximation, but since nested sampling is not producing an unbiased estimator of the evidence Z, the point is somewhat moot. (I am also rather surprised by the reported lack of computing time benefit in running ABC-SMC.)

## One World ABC seminar [31.3.22]

Posted in Statistics, University life with tags ABC, Approximate Bayesian computation, approximate inference, computer simulation, One World, One World ABC Seminar, QUT, rejection sampling, University of Warwick, webinar on March 16, 2022 by xi'an**T**he next One World ABC seminar is on Thursday 31 March, with David Warnes (from QUT) talking on Multifidelity multilevel Monte Carlo for approximate Bayesian computation It will take place at 10:30 CET (GMT+1).

Models of stochastic processes are widely used in almost all fields of science. However, data are almost always incomplete observations of reality. This leads to a great challenge for statistical inference because the likelihood function will be intractable for almost all partially observed stochastic processes. As a result, it is common to apply likelihood-free approaches that replace likelihood evaluations with realisations of the model and observation process. However, likelihood-free techniques are computationally expensive for accurate inference as they may require millions of high-fidelity, expensive stochastic simulations. To address this challenge, we develop a novel approach that combines the multilevel Monte Carlo telescoping summation, applied to a sequence of approximate Bayesian posterior targets, with a multifidelity rejection sampler that learns from low-fidelity, computationally inexpensive,

model approximations to minimise the number of high-fidelity, computationally expensive, simulations required for accurate inference. Using examples from systems biology, we demonstrate improvements of more than two orders of magnitude over standard rejection sampling techniques