Archive for ABC model selection

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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BayesComp 2025.4

Posted in pictures, Running, Statistics, Travel, University life with tags , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , on June 21, 2025 by xi'an

The third and final day of the (main) conference started tih Emtiyaz Khan’s plenary talk on adaptive Bayesian intelligence. Or, imho, [adaptive [Bayesian]] intelligence, with the brackets indicating redundancy since intelligence need include adaptivity and [intelligent] adaptivity need proceed in a Bayesian way! Focussing first on the Bayesian learning rule via variational Bayes (with a stress on Kingma’s 1994 Adam optimisation algorithm, the “most cited paper” [in machine learning]) where learning boils down to gradient steps (due to the exponential family structure), themselves versions of Taylor (or Laplace) approximations). With an interesting vision of Bayesian updating as accounting for prediction mismatch. (I missed the connection Roberta in IMDb appearing in one slide!)

 The following session offered no dilemma [sorry, Alex, Axel, Chris, Robert, Sumeet, Victor!] since it included the federated learning session I organised, with Louis Asslet, Conor Hassan, and Jean-Michel Marin as speakers. Louis’ talk was on confidential [homomorphic] accept-reject algorithms to learn from other sources, while preserving (differential?) privacy, part of which came during Les Houches workshops I organised this Spring and the one before. Exploiting the additive features of log-likelihoods and exponential variates and adopting a testing perspective on privacy. Conor motivated his model with the Australian cancer atlas project Kerrie Mengersen and others have been developing over the years. The federated approach relies on variational approximations that return the same answer as an exact resolution, but more efficiently. (From a privacy perspective, I wonder at the impact of variational approximations on protecting the data, which boils down to a choice of (sufficient) statistics for the exponential families behind those approximations.) For more complicated models incorporating spatial dependence prohibits full Bayesian inference, unfortunately. Jean-Michel commented on the richness of methods for simulation-based inference, incl. model choice. His focus was on using sequential neural likelihood estimation and sequential importance sampling to approximate evidence. As in the Read Paper of Del Moral et al. (2006). Mentioning a neural version of the harmonic mean estimator by Spurio Mancini et al.  (2023)! I wondered at the degree of (Rao-Blackwell) recycling involved in the computation, Jean-Michel’s answer being that AMIS is soon coming [in a theatre near you!].

The afternoon sessions did offer any reprieve in the choice of topic! I first went to Approximate Methods for Accelerated Sampling, with Rong Tang evaluating the informativeness of summary statistics through a divergence evaluation. Using autoencoders to replace the intractable posterior, with sliced minimal model discrepancy (MMD) and (pseudo?) score matching loss for divergences (reminding me of indirect inference and synthetic likelihood). Yun Yang discussed a variational proposal to estimate the number of components in a mixture model. Surprising given the multimodal structure of mixture posteriors. And the overall irregularity of (evil!) mixture models. But I could not figure out from the talk the form of the approximation.

On the food scene, tasted a nice and spicy Peranakan rice vermicelli dish called Mee Siam yesterday in a campus restaurant, which sustained me fore the rest of the day, including the ABC s/webinar. And another spicy hot pot today at NUS, to catch up on veggies, while missing the chili crab local specialty on that trip.

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BayesComp 2025.3

Posted in pictures, Running, Statistics, Travel, University life with tags , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , on June 20, 2025 by xi'an

The second day of the conference started with a cooler and less humid weather (although this did not last!), although my brain felt a wee bit foggy from a lack of sleep (and I almost crashed while running on the hotel treadmill, at 14.5km/h!), and the plenary talk of my friend of many years Sylvia Früwirth-Schnatter on horseshoe priors and time-varying time series (à la West). With a nice closed-form representation involving hypergeometric functions of the second kind (my favourite!), with the addition of a triple-Gamma prior. Sylvia stressed on the enormous impact of the prior choice on change-point detection, which was already the point in the original horseshoe paper (as opposed to George’s Lasso prior). Without incorporating any specific modelling on potential change-point, fair enough given that the parameter is moving with time, unhindered. Her MCMC choices involved discrete parameters with Negative Binomial and Poisson parameters, allowing for partially integrated or collapsed solutions. Possibly further improved by Swendsen-Wang steps.

I then attended the (advanced) Langevin session after agonising upon my choice for a wealth of options! Sam Power presented a talk linking simulation with optimisation targets, over measure spaces. With Wasserstein gradient flow algorithms that resemble Langevin algorithms once discretised by a particle system. (A natural resolution producing a somewhat unnatural form of measure estimator since made of Dirac masses, from which very little can be learned.) Then [my Warwick colleague & coauthor] Any Wang on underdamped Langevin diffusions. when Poincaré‘s inequality fails, but convergence (in total variation) still occurs. Followed by Peter Whalley on splitting methods (where random hypergeometric subsampling dominates Robbins-Monro) and stochastic gradient algorithms, in a connected (to the previous talks) way since involving underdamped aspects. (With a personal discovery of Polyak’s heavy ball method.)

The afternoon session saw me facing a terrible dilemma with three close friends talking at the same time! Eventually opting for PDMPs, over simulation-based inference and recalibration for approximate Bayesian methods. Kengo Kamatani gave a general introduction to PDMPs, before explaining the automated implementation he considered with Charly Andral (during Charly’s visit to ISM, Tokyo, two summers ago). Towards accelerating the generation of the jump time. Then Luke Hardcastle applied PDMPs for survival prediction, using spike & slab priors and sticky PDMPs. And Jere Koskela (formerly Warwick) extended zig-zag sampling to discrete settings (incl. Kingman’s coalescent.)

The (rather long) day was not over yet since we had planned an extra on-site OWABI seminar & webinar with two participants in the conference, Filippo Pagani (Warwick and OCEAN postdoc) using fusion for federated learning, with a trapezoidal approximation, and Maurizio Filippone on GANs as hidden perfect ABC model selection, a GAN providing an automatic density estimator… With astounding Gemini-generated cartoons! Videos are soon to be available. A big congrats to the speakers who managed to convey their ideas and results despite the late hour! (On the extra-academic side, I was invited last night to a genuine Szechuan dinner in Chinatown, with a large array of spicy dishes if not that spicy!, and a rare opportunity to taste abalone. And bullfrogs. Quite a treat! And a good reason to skip dinner altogether!)

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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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Approximate Bayesian model choice

Posted in Books, R, Statistics, Travel, University life with tags , , , , , , , , , on March 17, 2014 by xi'an

The above is the running head of the arXived paper with full title “Implications of  uniformly distributed, empirically informed priors for phylogeographical model selection: A reply to Hickerson et al.” by Oaks, Linkem and Sukuraman. That I (again) read in the plane to Montréal (third one in this series!, and last because I also watched the Japanese psycho-thriller Midsummer’s Equation featuring a physicist turned detective in one of many TV episodes. I just found some common features with The Devotion of Suspect X, only to discover now that the book has been turned into another episode in the series.)

“Here we demonstrate that the approach of Hickerson et al. (2014) is dangerous in the sense that the empirically-derived priors often exclude from consideration the true values of the models’ parameters. On a more fundamental level, we question the value of adopting an empirical Bayesian stance for this model-choice problem, because it can mislead model posterior probabilities, which are inherently measures of belief in the models after prior knowledge is updated by the data.”

This paper actually is a reply to Hickerson et al. (2014, Evolution), which is itself a reply to an earlier paper by Oaks et al. (2013, Evolution). [Warning: I did not check those earlier references!] The authors object to the use of “narrow, empirically informed uniform priors” for the reason reproduced in the above quote. In connection with the msBayes of Huang et al. (2011, BMC Bioinformatics). The discussion is less about ABC used for model choice and posterior probabilities of models and more about the impact of vague priors, Oaks et al. (2013) arguing that this leads to a bias towards models with less parameters, a “statistical issue” in their words, while Hickerson et al. (2014) think this is due to msBayes way of selecting models and their parameters at random.

“…it is difficult to choose a uniformly distributed prior on divergence times that is broad enough to confidently contain the true values of parameters while being narrow enough to avoid spurious support of models with less parameter space.”

So quite an interesting debate that takes us in fine far away from the usual worries about ABC model choice! We are more at the level empirical versus natural Bayes, seen in the literature of the 80’s. (The meaning of empirical Bayes is not that clear in the early pages as the authors seem to involve any method using the data “twice”.) I actually do not remember reading papers about the formal properties of model choice done through classical empirical Bayes techniques. Except the special case of Aitkin’s (1991,2009) integrated likelihood. Which is essentially the analysis performed on the coin toy example (p.7)

“…models with more divergence parameters will be forced to integrate over much greater parameter space, all with equal prior density, and much of it with low likelihood.”

The above argument is an interesting rephrasing of Lindley’s paradox, which I cannot dispute, but of course it does not solve the fundamental issue of how to choose the prior away from vague uniform priors… I also like the quote “the estimated posterior probability of a model is a single value (rather than a distribution) lacking a measure of posterior uncertainty” as this is an issue on which we are currently working. I fully agree with the statement and we think an alternative assessment to posterior probabilities could be more appropriate for model selection in ABC settings (paper soon to come, hopefully!).

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