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 prequential loss
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'anISBA⁶
Posted in pictures, Running, Statistics, Travel, University life with tags adaptive MCMC, curry, doubly intractable posterior, embarrassingly parallel MCMC, fish market, food poisoning, GPU, hitsumabushi, ISBA 2026, ISBA 2028, Japan, label switching, logo, MCMC, mirror workshop, mixtures of distributions, Nagoya Castle, noise contrasting estimation, prequential loss, quadrature, Shinkansen, simulated annealing, SMC, stereographic MCMC, udon, Valencia conferences, Venice, Wisconsin on July 5, 2026 by xi'an
After a final early morning run in the rising sun, reaching a point north of the city where I could see a nearby volcano (not Fuji-san!), I attended both morning on MCMC, with (again) a range of interesting, mostly novel, questions and solutions. With no overlap with his talk at mostly Monte Carlo last month, Sam Livingstone gave convincing motivations for using new tools for designing proper scaling (in the limit) for some adaptive MCMC. Charles Margossian’s talk was particularly exciting for pushing for single step MCMC when massively run in parallel, provided warm-up is over (enough). And Saif Syed discussing a new version of annealed SMC, using the variability of the estimated normalising constant as an assessment of the (although I could not catch how the tridimensional calibration was handled). I was less convinced by Kyle Kuang’s approach to overcome identifiability issues such as label switching, as it sounded too simple to be universally applicable. Bingjing Tang returned to the challenge of doubly intractable posteriors. With motivations from functional inference and a solution reminding me of noise contrastive estimation. until I spoke with the authors and realised it was much closer to our recent paper with Edoardo and Julien. While Bjorn Sprungk’s talk on Metropolized interacting particle sampling reminded me of our pinball sampler, presented… 30 years ago at the 1996 Valencia meeting! But using the product of posteriors as a target sounds suboptimal when a target that would keep particles apart (with the correct marginals) would prove more exploratory.
The noon break was the last opportunity to sample one of the food stalls in the fish market nearby, with a spicy curry udon bowl. Cutting the eel addiction!
My final session—before catching a shinkansen to Tokyo for the Information Geometry, Privacy and Monte Carlo ISBA Satellite Meeting at the Institute of Statistical Mathematics—was about loss-based posteriors, with our PhD student Shreya Roy presenting her work on prequential posteriors. And Kshitij Khare on using a loss that allows for a regular Gibbs sampler implementation via a pseudo-model and consistency properties.
This cuvée of ISBA World Meeting was exceptionally (gouleyante and) enjoyable (except for my recurrent sleeping issues) from the diverse and well-balanced programme, to the choice of plenary speakers, to the practicality of the conference centre (except for the queues for the lift!) and its location in Nagoya, with its own, unsuspected, perks! With no food poisoning this time!! ISBA 2028 is scheduled to take place in Milwaukee and I am very unlikely to attend, unless a rogue mirror pops up!
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
prequential posteriors
Posted in Books, Statistics, University life with tags arXiv, Bayesian deep learning, data generating process, generalised Bayesian inference, ICSDS 2025, IMS, intractable likelihood, PhD students, prequential loss, probabilistic forecasting, Sevilla, SMC, Student Award, University of Warwick on December 15, 2025 by xi'an
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.
