One morning session on optimal transport after first-hand witnessing the impressive ballet of orderly lines entering the subway at Nagoya Station (and a very early run along the river and a high humidity rate, hence the picture of empty street at 5am). With Hugo Lavenant exhibiting optimal rates for Bayesian nonparametrics using Wasserstein distances, Pierre Jacob coupling MCMC chains, and Anya Katsevich investigating non-Gaussian asymptotic distributions in high dimensions (beyond Bernstein-von Mises). Then I tried to attend the session on Bayesian Uncertainty Quantification and Posterior Sampling for Large-Scale Generative Models, but it proved too popular for the number of seats, and I ended up discussing with others. After a nap related to my jetlag induced, early, rise I went back to chair Sid Chib’s Foundation Lecture, where he discussed the use of an orbit of models in Bayesian model choice, rather than the (MAP) most likely one. Based on their 2018 JASA paper which I already discussed in Paris with Anna Simoni presenting. Hence reminding me of points I presumably already made, from the issue of having too many models to realistically explore to constructing coherent priors across them, with the fractional, empirical, proxy of using a (same) fraction of the sample as a learning sample, to more philosophical issues like missing a utility function about having to chose a model, especially with all models being wrong, missing an uncertainty quantification on the evidence itself, rather than using most likely models (MAP!), called an orbit by Sid (which requires some calibration). Since the uncertainty represented by the sample induces an uncertainty in the ranking of models. And a most appropriate, almost local, occurrence of the Rashomon principle!!! And I finished the day mixing with many friends in the poster session¹, where Darren Wraith presented our ongoing work on novel, adaptive, importance, sampling.
Archive for model uncertainty
ISBA 2026²
Posted in Books, pictures, Running, Statistics, Travel, University life with tags Bayesian model averaging, Bayesian model choice, Bernstein-von Mises theorem, Chib's approximation, evidence, ISBA 2026, ISBA World Meeting, Japan, map, model uncertainty, Nagoya, Rashomon, Sid Chib, Wasserstein distance on July 1, 2026 by xi'ana guest post from Julyan Arbel on ISBA on-line resources
Posted in Books, pictures, Statistics, University life with tags ABC, Bayes World meeting, Bayesian Analysis, BioPharma, BNP, discussion paper, Helsinki, International Society for Bayesian Analysis, ISBA, j-ISBA, missing data, model uncertainty, petrol dealer, social med, webinar, youtube on September 30, 2025 by xi'anI would like to highlight two resources that, in my humble opinion as ISBA Social Media Manager, remain under-recognized yet immensely valuable:
ISBA Webinars on Bayesian Analysis Articles (2019–present).This webpage gathers an exceptional collection of webinars discussing Bayesian Analysis articles since 2019. For anyone curious about the frontiers of Bayesian statistics, this series brings together cutting-edge research from world-class experts. The talks span topics such as model uncertainty and missing data, new perspectives on stick-breaking models, sparse Bayesian factor analysis, and advances in causal inference under model mis-specification. Other contributions cover nonparametric priors, spatio-temporal modeling of Arctic sea ice, Bayesian regression trees for causal inference, and much more.The next BA webinar will focus on the paper “Model Uncertainty and Missing Data: An Objective Bayesian Perspective” by G. García-Donato, M. Eugenia Castellanos, S. Cabras, A. Quirós, and A. Forte. There will be four invited discussants: M. Clyde, M. Ferreira, A. Ly, and J. Rubio. It is scheduled for November 5, 2025 (4:00 PM UTC | 11:00 AM EST | 5:00 PM CET). Registration will be announced later on this webpage.ISBA YouTube Channel.All recorded webinar videos are available on the ISBA YouTube channel. Beyond the webinars, the channel hosts curated playlists from ISBA World Meetings (2012, 2016, 2018, 2021, 2022, 2024), specialized workshops and seminars (ABI, BNP, BayesComp), as well as content from ISBA Sections (j-ISBA, BNP, BioPharma, Industrial).These resources deserve broad visibility. I warmly encourage you to explore them, share them within your networks, and let us know your feedback.— Julyan, on behalf of the ISBA Social Media team
model uncertainty and missing data: an objective BAyesian perspective
Posted in Books, Statistics, Travel, University life with tags Arnold Zellner, Bayes factor, Bayesian Analysis, Bayesian model comparison, Bayesian predictive, Bayesian variable selection, deviance information criterion, DIC, Don Rubin, Florence Forbes, g-priors, Gilles Celeux, Haar measure, ignorability, improper priors, invariance, Jeffreys priors, linear regression, marginal likelihood, Mike Titterington, missing values, missing-at-random model, model uncertainty, objective Bayes, objective prior distribution, oracle, ozone dataset, reference prior, Rubin’s rules, Spain, time zones, webinar on September 16, 2025 by xi'an
My Spanish and objective Bayesian friends Gonzalo García-Donato, María Eugenia Castellanos, Stefano Cabras, Alicia Quirós, and Anabel Forte wrote an fairly exciting paper in BA that is open to discussion (for a few more days), to be discussed on 05 November (4:00 PM UTC | 11:00 AM EST | 5:00 PM CET).
The interplay between missing data and model uncertainty—two classic statistical problems—leads to primary questions that we formally address from an objective Bayesian perspective. For the general regression problem, we discuss the probabilistic justification of Rubin’s rules applied to the usual components of Bayesian variable selection, arguing that prior predictive marginals should be central to the pursued methodology. In the regression settings, we explore the conditions of prior distributions that make the missing data mechanism ignorable, provided that it is missing at random or completely at random. Moreover, when comparing multiple linear models, we provide a complete methodology for dealing with special cases, such as variable selection or uncertainty regarding model errors. In numerous simulation experiments, we demonstrate that our method outperforms or equals others, in consistently producing results close to those obtained using the full dataset. In general, the difference increases with the percentage of missing data and the correlation between the variables used for imputation.
The so-called Rubin’s identity is simply the representation of the posterior probability of a model γ given the observed data x⁰, p(γ|x⁰), as the integrated posterior probability of a model given both observed and latent data, p(γ|x⁰, x¹), against the marginal of latent x¹ given observed x⁰. Since this marginal involves the probabilities p(γ|x⁰), this representation is not directly useful for a numerical implementation.
In this paper, missingness relates to some entries of either the covariates or the response variate. Which is less common but more realistic, especially if some covariates do not contribute to the response. (The missingness mechanism does not matter if the data is missing at random (à la Rubin). The computational solution (p9) is rather standard, simulating the missing variables given the observed variables. In my opinion, the elephant in the room is the super-delicate selection of a prior distribution on the missing covariates, as methinks this impacts in a considerable manner the actual value of the Bayes factor, hence the selection of the surviving model. (As a side remark, we are credited in Celeux et al. (2006) to have “extended DIC for missing data models or when missing data were present”, but our point was instead to point out the arbitrariness of the very definition of DIC in such contexts.)
“The standard Bayesian method for addressing the absence of prior information uses improper distributions. In estimation problems (the model is fixed), the impropriety of priors does not imply any additional difficulty as long as the posterior is proper” (p9)
The authors point out the well-known difficulty with improper priors but still resort to improper priors on the parameters shared by all models—which I dispute as being adequate, despite the arguments put forward on p15, right Haar measure or not—, while sticking to proper priors on the model-dependent parameters. Which unsurprisingly become Zellner’s g-priors. Or rather g’-priors, although the discussion seems to resolve into the (model-free) factor g’ being equal to 1 as for the g-priors. Again a strong term in the derivation of the Bayes factor.
a case for Bayesian deep learnin
Posted in Books, pictures, Statistics, Travel, University life with tags Bayesian foundations, Bayesian model choice, Bayesian neural networks, Bayesian variable selection, Berlin Tegel flughafen, marginalisation, model uncertainty, noninformative priors, normalisation, objective Bayes, snowstorm on September 30, 2020 by xi'an
Andrew Wilson wrote a piece about Bayesian deep learning last winter. Which I just read. It starts with the (posterior) predictive distribution being the core of Bayesian model evaluation or of model (epistemic) uncertainty.
“On the other hand, a flat prior may have a major effect on marginalization.”
Interesting sentence, as, from my viewpoint, using a flat prior is a no-no when running model evaluation since the marginal likelihood (or evidence) is no longer a probability density. (Check Lindley-Jeffreys’ paradox in this tribune.) The author then goes for an argument in favour of a Bayesian approach to deep neural networks for the reason that data cannot be informative on every parameter in the network, which should then be integrated out wrt a prior. He also draws a parallel between deep ensemble learning, where random initialisations produce different fits, with posterior distributions, although the equivalent to the prior distribution in an optimisation exercise is somewhat vague.
“…we do not need samples from a posterior, or even a faithful approximation to the posterior. We need to evaluate the posterior in places that will make the greatest contributions to the [posterior predictive].”
The paper also contains an interesting point distinguishing between priors over parameters and priors over functions, ony the later mattering for prediction. Which must be structured enough to compensate for the lack of data information about most aspects of the functions. The paper further discusses uninformative priors (over the parameters) in the O’Bayes sense as a default way to select priors. It is however unclear to me how this discussion accounts for the problems met in high dimensions by standard uninformative solutions. More aggressively penalising priors may be needed, as those found in high dimension variable selection. As in e.g. the 10⁷ dimensional space mentioned in the paper. Interesting read all in all!
can we trust computer simulations?
Posted in Books, pictures, Statistics, University life with tags atmospheric models, Bayesian epistemology, climate simulation, computer model, conference, confirmation, epistemology, Fortran, Hannover, Hempel, Hertzsprung-Russell diagram, Karl Popper, model uncertainty, Monash University, philosophy of sciences, scientific computing, Society for Imprecise Probability, truth, validation, verification on July 10, 2015 by xi'an
How can one validate the outcome of a validation model? Or can we even imagine validation of this outcome? This was the starting question for the conference I attended in Hannover. Which obviously engaged me to the utmost. Relating to some past experiences like advising a student working on accelerated tests for fighter electronics. And failing to agree with him on validating a model to turn those accelerated tests within a realistic setting. Or reviewing this book on climate simulation three years ago while visiting Monash University. Since I discuss in details below most talks of the day, here is an opportunity to opt away! Continue reading
