Archive for likelihood-free methods

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tenets of quantile-based inference in Bayesian models

Posted in Books, Statistics with tags , , , , , , , , , , , , , , on June 8, 2025 by xi'an

This 2023 paper of Perepolkin, Goodrich, and Sahlin vaguely relates to our insufficient Gibbs work in that a Bayesian analysis is conducted based solely on quantile summaries. Except that here the input is the entire cdf, or the—inverse cdf—quantile function, or—its derivative—the quantile density function, instead of the probability density function—used as the likelihood in the posterior. Which is a non-problem from a mathematical perspective since all these functions describe the same probability distribution. Which makes the following quote rather puzzling (in its obviousness).

“We aim to show that the quantile-based Bayesian inference using the intermediate depths leads to the same posterior beliefs as the conventional density-based inference.”

The authors still make a big case of the difference, obviously, to the point of proposing a different notation for Y~F. But using the same symbol f for different densities. The formal expression of the posterior based on the quantile function actually requires the cdf function and the density or the quantile density to be available (at least in a numerical sense), witness eqn (11).

The paper still could hold some interest in its computational component. Relating to ABC, obviously, since distributions defined by quantiles and cdfs often come as benchmarks for ABC, when the associated pdf/likelihood is unavailable. Witness g-and-k distributions (with the caveat MCMC can be implemented in this case). Unfortunately, the paper entirely relies on numerical inversion (with a puzzling comment that MCMC rejection gets higher with numerical inversion, p6). And only mentions ABC in the conclusion, possibly to pacify a referee’s comment. And actually consider that “quantile parameterized quantile distributions don’t lend themselves easily as sampling distributions due to the special nature of their parameterization” (p4). Hence making me wonder at the overall relevance of the entire endeavour….

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Marc Beaumont on One World ABC webinar [30 May, 9am]

Posted in Books, pictures, Statistics, Travel, University life with tags , , , , , , , , , , , on May 17, 2024 by xi'an

For the final talk of this Spring season of the One World ABC webinar, we are very glad to welcome Marc Beaumont, a central figure in the development of ABC methods and inference! (And a coauthor of our ABC-PMC paper.)

Model misspecification in population genomic
Mark Beaumont
University of Bristol
30th May 2024, 9.00am UK time

Abstract
In likelihood-free settings, problematic effects of model misspecification can manifest themselves during computation, leading to nonsensical answers, particularly causing convergence problems in sequential algorithms. This issue has been well studied in the last 10 years, leading to a number of methods for robust inference. In practical applications, likelihood-free methods tend to be applied to the output of complex simulations where there is a choice of summary statistics that can be computed. One approach to handling misspecification is to simply not use summary statistics computed from simulations of the model under the prior that cannot be with those observed in the data. This presentation gives a brief review of methods for observing and handling misspecification in ABC and SBI, and then discusses approaches that we have explored in a population genomic modelling framework.

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a versatile alternative to ABC

Posted in Books, Statistics with tags , , , , , , , , , on July 25, 2023 by xi'an

“We introduce the Fixed Landscape Inference MethOd, a new likelihood-free inference method for continuous state-space stochastic models. It applies deterministic gradient-based optimization algorithms to obtain a point estimate of the parameters, minimizing the difference between the data and some simulations according to some prescribed summary statistics. In this sense, it is analogous to Approximate Bayesian Computation (ABC). Like ABC, it can also provide an approximation of the distribution of the parameters.”

I quickly read this arXival by Monard et al. that is presented as an alternative to ABC, while outside a Bayesian setup. The central concept is that a deterministic gradient descent provides an optimal parameter value when replacing the likelihood with a distance between the observed data and simulated synthetic data indexed by the current value of the parameter (in the descent). In order to operate the descent the synthetic data is assumed to be available as a deterministic transform of the parameter value and of a vector of basic random objects, eg Uniforms. In order to make the target function differentiable, the above Uniform vector is fixed for the entire gradient descent. A puzzling aspect of the paper is that it seems to compare the (empirical) distribution of the resulting estimator with a posterior distribution, unless the comparison is with the (empirical) distribution of the Bayes estimators. The variability due to the choice of the fixed vector of basic random objects does not seem to be taken into account either, apparently. Furthermore, the method is presented as able to handle several models at once, which I find difficult to fathom as (a) the random vectors behind each model necessarily vary and (b) there is no apparent penalisation for complexity.

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ABC in Lapland²

Posted in Mountains, pictures, Statistics, University life with tags , , , , , , , , , , , , , , , , , , , , on March 16, 2023 by xi'an

On the second day of our workshop, Aki Vehtari gave a short talk about his recent works on speed up post processing by importance sampling a simulation of an imprecise version of the likelihood until the desired precision is attained, importance corrected by Pareto smoothing¹⁵. A very interesting foray into the meaning of practical models and the hard constraints on computer precision. Grégoire Clarté (formerly a PhD student of ours at Dauphine) stayed on a similar ground of using sparse GP versions of the likelihood and post processing by VB²³ then stir and repeat!

Riccardo Corradin did model-based clustering when the nonparametric mixture kernel is missing a normalizing constant, using ABC with a Wasserstein distance and an adaptive proposal, with some flavour of ABC-Gibbs (and no issue of label switching since this is clustering). Mixtures of g&k models, yay! Tommaso Rigon reconsidered clustering via a (generalised Bayes à la Bissiri et al.) discrepancy measure rather than a true model, summing over all clusters and observations a discrepancy between said observation and said cluster. Very neat if possibly costly since involving distances to clusters or within clusters. Although she considered post-processing and Bayesian bootstrap, Judith (formerly [?] Dauphine)  acknowledged that she somewhat drifted from the theme of the workshop by considering BvM theorems for functionals of unknown functions, with a form of Laplace correction. (Enjoying Lapland so much that I though “Lap” in Judith’s talk was for Lapland rather than Laplace!!!) And applications to causality.

After the (X country skiing) break, Lorenzo Pacchiardi presented his adversarial approach to ABC, differing from Ramesh et al. (2022) by the use of scoring rule minimisation, where unbiased estimators of gradients are available, Ayush Bharti argued for involving experts in selecting the summary statistics, esp. for misspecified models, and Ulpu Remes presented a Jensen-Shanon divergence for selecting models likelihood-freely²², using a test statistic as summary statistic..

Sam Duffield made a case for generalised Bayesian inference in correcting errors in quantum computers, Joshua Bon went back to scoring rules for correcting the ABC approximation, with an importance step, while Trevor Campbell, Iuri Marocco and Hector McKimm nicely concluded the workshop with lightning-fast talks in place of the cancelled poster session. Great workshop, in my most objective opinion, with new directions!

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ABC in Lapland

Posted in Mountains, pictures, Statistics, University life with tags , , , , , , , , , , , , , , , , on March 15, 2023 by xi'an

Greetings from Levi, Lapland! Sonia Petrone beautifully started the ABC workshop with a (the!) plenary Sunday night talk on quasi-Bayes in the spirit of both Fortini & Petrone (2020) and the more recent Fong, Holmes, and Walker (2023). The talk got me puzzled by wondering the nature of convergence, in that it happens no matter what the underlying distribution (or lack thereof) of the data is, in that, even without any exchangeability structure, the predictive is converging. The quasi stems from a connection with the historical Smith and Markov (1978) sequential update approximation for the posterior attached with mixtures of distributions. Which itself relates to both Dirichlet posterior updates and Bayesian bootstrap à la Newton & Raftery. Appropriate link when the convergence seems to stem from the sequence of predictives instead of the underlying distribution, if any, pulling Bayes by its own bootstrap…! Chris Holmes also talked the next day about this approach, esp. about a Bayesian approach to causality that does not require counterfactuals, in connection with a recent arXival of his (on my reading list).

Carlo Alberto presented both his 2014 SABC (simulated annealing) algorithm with a neat idea of reducing waste in the tempering schedule and a recent summary selection approach based on an auto-encoder function of both y and noise to reduce to sufficient statistic. A similar idea was found in Yannik Schälte’s talk (slide above). Who was returning to Richard Wiilkinson’s exact ABC¹³ with adaptive sequential generator, also linking to simulated annealing and ABC-SMC¹² to the rescue. Notion of amortized inference. Seemingly approximating data y with NN and then learn parameter by a normalising flow.

David Frazier talked on Q-posterior²³ approach, based on Fisher’s identity, for approximating score function, which first seemed to require some exponential family structure on a completed model (but does not, after discussing with David!), Jack Jewson on beta divergence priors²³ for uncertainty on likelihoods, better than KLD divergence on e-contamination situations, any impact on ABC? Masahiro Fujisawa back to outliers impact on ABC, again with e-contaminations (with me wondering at the impact of outliers on NN estimation).

In the afternoon session (due to two last minute cancellations, we skipped (or [MCMC] skied) one afternoon session, which coincided with a bright and crispy day, how convenient! ), Massi Tamborino (U of Warwick) FitzHugh-Nagumo process, with impossibilities to solve the inference problem differently, for instance Euler-Maruyama does not always work, numerical schemes are inducing a bias. Back to ABC with the hunt for a summary that get rid of the noise, as in Carlo Alberto’s work. Yuexi Wang talked about her works on adversarial ABC inspired from GANs. Another instance where noise is used as input. True data not used in training? Imke Botha discussed an improvement to ensemble Kalman inversion which, while biased, gains over both regular SMC timewise and ensemble Kalman inversion in precision, and Chaya Weerasinghe focussed on Bayesian forecasting in state space models under model misspecification, via approximate Bayesian computation, using an auxiliary model to produce summary statistics as in indirect inference.

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