Archive for Approximate Bayesian computation

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likelihood-free posterior density learning at OWABI [30 April, 1pm GMT+1, 2pm CEST, 8am EST]

Posted in pictures, Running, Statistics, Travel, University life with tags , , , , , , , , , , , , , , , , on April 17, 2026 by xi'an

The next OWABI webinar will take place on 30 April, at 1pm Coventry time (2pm in Paris, 8am in Columbus, Ohio) and will feature

Oksana A. Chkrebtii (Ohio State University)

Likelihood-free Posterior Density Learning for Uncertainty Quantification in Inference Problems
Generative models and those with computationally intractable likelihoods are widely used to describe complex systems in the natural sciences, social sciences, and engineering. Fitting these models to data requires likelihood-free inference methods that explore the parameter space without explicit likelihood evaluations, relying instead on sequential simulation, which comes at the cost of computational efficiency and extensive tuning. We develop an alternative framework called kernel-adaptive synthetic posterior estimation (KASPE) that uses deep learning to directly reconstruct the mapping between the observed data and a finite-dimensional parametric representation of the posterior distribution, trained on a large number of simulated datasets. We provide theoretical justification for KASPE and a formal connection to the likelihood-based approach of expectation propagation. Simulation experiments demonstrate KASPE’s flexibility and performance relative to existing likelihood-free methods including approximate Bayesian computation in challenging inferential settings involving posteriors with heavy tails, multiple local modes, and over the parameters of a nonlinear dynamical system.

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Approximate Bayesian Computation with Statistical Distances for Model Selection [OWABI, 27 Nov]

Posted in Books, Statistics, University life with tags , , , , , , , , , , , , , , on November 17, 2025 by xi'an

The next OWABI seminar is delivered by Clara Grazian (University of Sidney), who will talk about “Approximate Bayesian Computation with Statistical Distances for Model Selection” on Thursday 27 November at 11am UK time:

Abstract: Model selection is a key task in statistics, playing a critical role across various scientific disciplines. While no model can fully capture the complexities of a real-world data-generating process, identifying the model that best approximates it can provide valuable insights. Bayesian statistics offers a flexible framework for model selection by updating prior beliefs as new data becomes available, allowing for ongoing refinement of candidate models. This is typically achieved by calculating posterior probabilities, which quantify the support for each model given the observed data. However, in cases where likelihood functions are intractable, exact computation of these posterior probabilities becomes infeasible. Approximate Bayesian computation (ABC) has emerged as a likelihood-free method and it is traditionally used with summary statistics to reduce data dimensionality, however this often results in information loss difficult to quantify, particularly in model selection contexts. Recent advancements propose the use of full data approaches based on statistical distances, offering a promising alternative that bypasses the need for handcrafted summary statistics and can yield posterior approximations that more closely reflect the true posterior under suitable conditions. Despite these developments, full data ABC approaches have not yet been widely applied to model selection problems. This paper seeks to address this gap by investigating the performance of ABC with statistical distances in model selection. Through simulation studies and an application to toad movement models, this work explores whether full data approaches can overcome the limitations of summary statistic-based ABC for model choice.
Keywords: model choice, distance metrics, full data approaches
Reference: C. Grazian, Approximate Bayesian Computation with Statistical Distances for Model Selection, preprint at ArXiv:2410.21603, 2025

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permutations accelerate ABC!

Posted in Books, Kids, pictures, Statistics, University life with tags , , , , , , , , , , , , , , , , , , , , , , on July 9, 2025 by xi'an

Yesterday a arXival by Antoine Luciano, Charly Andral (both PhD students, now or then, at Paris Dauphine), Robin Ryder (formerly at Paris Dauphine, now at Imperial College London) and myself got posted. It proposes to improve the scalability of ABC methods by exploiting the (full or partial) exchangeability in the data by implementing permutation-based matching between observed and simulated samples. This significantly improves computational efficiency, which is further enhanced by sequential strategies such as over-sampling, which facilitates early-stage acceptance by temporarily increasing the number of simulated compartments, and under-matching, which relaxes the acceptance condition by matching only subsets of the data. The map of France appears in connection with an application of the method to estimating SIR parameters, department by department. (It is also reminding me of the cover of Markov Chain Monte Carlo methods in practice, the 1996 contributed book edited by Wally Gilks, Sylvia Richardson and David Spiegelhalter.)

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exceptional OWABI web/sem’inar [19 June, BayesComp²⁵]

Posted in pictures, Statistics, Travel, Uncategorized, University life with tags , , , , , , , , , , , , , , on June 10, 2025 by xi'an


Exceptionally, the next One World Approximate Bayesian Inference (OWABI) Seminar will be hybrid as it is scheduled to take place during BayesComp 2025 in Singapore, on Thursday 19 June at 8pm Singapore time (1pm in Tórshavn) and two talks, one by Filippo Pagani on

Approximate Bayesian Fusion
Bayesian Fusion is a powerful approach that enables distributed inference while maintaining exactness. However, the approach is computationally expensive. In this work, we propose a novel method that incorporates numerical approximations to alleviate the most computationally expensive steps, thereby achieving substantial reductions in runtime. Our approach retains the flexibility to approximate the target posterior distribution to an arbitrary degree of accuracy, and is scalable with respect to both the size of the dataset and the number of computational cores. Our method offers a practical and efficient alternative for large-scale Bayesian inference in distributed environments.
and one by Maurizio Filippone on
GANs Secretly Perform Approximate Bayesian Model Selection
Generative Adversarial Networks (GANs) are popular models achieving impressive performance in various generative modeling tasks. In this work, we aim at explaining the undeniable success of GANs by interpreting them as probabilistic generative models. In this view, GANs transform a distribution over latent variables Z into a distribution over inputs X through a function parameterized by a neural network, which is usually referred to as the generator. This probabilistic interpretation enables us to cast the GAN adversarial-style optimization as a proxy for marginal likelihood optimization. More specifically, it is possible to show that marginal likelihood maximization with respect to model parameters is equivalent to the minimization of the Kullback-Leibler (KL) divergence between the true data generating distribution and the one modeled by the GAN. By replacing the KL divergence with other divergences and integral probability metrics we obtain popular variants of GANs such as f-GANs, Wasserstein-GANs, and Maximum Mean Discrepancy (MMD)-GANs. This connection has profound implications because of the desirable properties associated with marginal likelihood optimization, such as (i) lack of overfitting, which explains the success of GANs, and (ii) allowing for model selection, which opens to the possibility of obtaining parsimonious generators through architecture search.

These talks will be delivered on-site and on-line, as a Zoom visio-conference.

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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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