The paper Prequential posteriors Shreya Roy wrote as part of her PhD thesis at Warwick U, under the supervision of Rito Dutta, Richard Everitt and myself, got published on-line after earlier acceptance by the Japanese Journal of Statistics and Data Science, an official journal of the Japanese Federation of Statistical Science Associations. Coïncidental but unrelated to my Akaike Memorial Lecture prize. The paper will be part of a special issue on Recent Advances in Dynamical Monte Carlo Methods. Congrats to Shreya, soon to defend her viva in Warwick!
Archive for generalised Bayesian inference
prequential posteriors in the Japanese Journal of Statistics and Data Science
Posted in Books, Statistics, Travel, University life with tags Akaike Lecture, data assimilation, deep generative forecasting models, defense, generalised Bayesian inference, generative models, intractable likelihood, Japan, Japanese Federation of Statistical Science Associations, Japanese Journal of Statistics and Data Science, Monte Carlo methods, prequential loss, prequential priors, publication, sequential Monte Carlo, special issue, viva on September 22, 2026 by xi'anOWABI⁷, 25 March 2026: Robust Simulation Based Inference (10am EST time)
Posted in Books, Statistics, University life with tags ABC, approximate Bayesian inference, arXiv, Carnegie Mellon University, exponential tilting, generalised Bayesian inference, generative model, Larry Wasserman, maximum mean discrepancy, model misspecification, OWABI, robust Bayesian procedures, Safe Anytime-Valid Inference, simulation-based inference, University of Warwick, webinar on March 9, 2026 by xi'an
Speaker: Larry Wasserman (Carnegie Mellon University)
Title: Robust Simulation Based Inference
Abstract: Simulation-Based Inference (SBI) is an approach to statistical inference where simulations from an assumed model are used to construct estimators and confidence sets. SBI is often used when the likelihood is intractable and to construct confidence sets that do not rely on asymptotic methods or regularity conditions. Traditional SBI methods assume that the model is correct, but, as always, this can lead to invalid inference when the model is misspecified. This paper introduces robust methods that allow for valid frequentist inference in the presence of model misspecification. We propose a framework where the target of inference is a projection parameter that minimizes a discrepancy between the true distribution and the assumed model. The method guarantees valid inference, even when the model is incorrectly specified and even if the standard regularity conditions fail. Alternatively, we introduce model expansion through exponential tilting as another way to account for model misspecification. We also develop an SBI based goodness-of-fit test to detect model misspecification. Finally, we propose two ideas that are useful in the SBI framework beyond robust inference: an SBI based method to obtain closed form approximations of intractable models and an active learning approach to more efficiently sample the parameter space.
Keywords: Exponential tilting, model misspecification, robust inference, simulation based inference, valid inference.
Reference: Lorenzo Tomaselli, Valérie Ventura, Larry Wasserman. Robust Simulation Based Inference. Preprint at ArXiv:2508.02404
OWABI⁷, 26 February 2026: Prequential posteriors (11am UK time)
Posted in Books, Statistics, University life with tags ABC, approximate Bayesian inference, diffusion model, generalised Bayesian inference, generative model, OWABI, prequential loss, reinforcement learning, score function, sequential ABC, sequential Monte Carlo, simulation-based inference, SMC, University of Warwick, webinar on February 25, 2026 by xi'an
Speaker: Shreya Sinha Roy (University of Warwick)
Title: Prequential posteriors
Abstract: Data assimilation is a fundamental task in updating forecasting models upon observing new data, with applications ranging from weather prediction to online reinforcement learning. Deep generative forecasting models (DGFMs) have shown excellent performance in these areas, but assimilating data into such models is challenging due to their intractable likelihood functions. This limitation restricts the use of standard Bayesian data assimilation methodologies for DGFMs. To overcome this, we introduce prequential posteriors, based upon a predictive-sequential (prequential) loss function; an approach naturally suited for temporally dependent data which is the focus of forecasting tasks. Since the true data-generating process often lies outside the assumed model class, we adopt an alternative notion of consistency and prove that, under mild conditions, both the prequential loss minimizer and the prequential posterior concentrate around parameters with optimal predictive performance. For scalable inference, we employ easily parallelizable wastefree sequential Monte Carlo (SMC) samplers with preconditioned gradient-based kernels, enabling efficient exploration of high-dimensional parameter spaces such as those in DGFMs. We validate our method on both a synthetic multi-dimensional time series and a real-world meteorological dataset; highlighting its practical utility for data assimilation for complex dynamical systems.
Keywords: diffusion models, simulation based inference, sequential methods.
Reference: S. S. Roy, R. Everitt, C. P Robert, R. Dutta. Prequential posteriors. Preprint at ArXiv:2511.17721, 202
When Is Generalized Bayes Bayesian?
Posted in Books, Statistics, University life with tags ABC, Bayes factors, Bayesian model choice, coherence, decision theory, generalised Bayesian inference, loss functions, marginal likelihood, normalising constant on February 13, 2026 by xi'an
I spotted this title in the new arXiv postings on Monday. When Is Generalized Bayes Bayesian? A Decision-Theoretic Characterization of Loss-Based Updating by Kenichiro McAlinn & Kōsaku Takanashi is discussing decision-theoretic consequences of generalized Bayes approaches based on losses and show that decisions based on a loss-based posterior coincides with those of ordinary Bayes if and only if the loss is essentially a negative log-likelihood (leading to a belief posterior). This is not very surprising in that, otherwise, there is no Bayesian update delivering the generalised Bayes pseudo-posteriors (which can be traced back to a 2007 result of Catoni). The authors also demonstrate that generalized marginal likelihoods are not delivering evidence for decision posteriors, and thus that Bayes factors are not well-defined in this context, which reminds me of our warning for ABC model choice. However, the reason here is much more mundane, as it is due to the decision posterior failing to identify the normalising constant Z(x). Outside belief posteriors. The paper concludes with a coherence book, which is a table reproduced above.
back to shrinkage!
Posted in Books, Statistics, University life with tags Bayesian lasso, generalised Bayesian inference, generative model, Gibbs sampling, intractable likelihood, MathPhDInFrance, Rouen, shrinkage, Université de Rouen, University of Warwick, Warwickshire on February 12, 2026 by xi'an
Our Warwick PhD student Shreya Sinha-Roy—who is now looking for a postdoctoral position next semester!—, along with Sherman Khoo, Ritabrata Dutta and myself, has now completed a paper on shrinkage priors for implicit generative models. That is, models based on deep neural networks and hence associated with intractable likelihoods. The work centres on developing and assessing an efficient training mechanism for these models, leveraging on tools from Bayesian model averaging using shrinkage (yay!) priors inspired from Lasso (rather than from my PhD years!) and generalized Bayes. In this large p (dimension of parameters) and small n (sample size of data) scenario, those sparsity inducing priors have been successfully used for linear regression when p is much larger than n, but have not been applied to implicit generative models due to the intractability of the likelihood function of the parameters of the model given observed data. Adapting a scoring rule posterior based on a strictly proper scoring rule as in generalized Bayes, we propose a block SGMCMC within Gibbs sampling mechanism to handle high dimensional parameter space for learning a sparse Bayesian model averaged neural implicit generative model in a sample efficient way. We illustrate excellent performance of our proposed method for p (much larger than n) linear regressions and three applications of neural generative models in tasks relevant to weather forecasting to reinforcement learning
