Prequential posteriors
stat.ML, cs.LG
Submitted: 2025-11-21
Updated: 2026-08-28
Journal ref: Japanese Journal of Statistics and Data Science (10 September 2026)
DOI: 10.1007/s42081-026-00374-w
License: http://creativecommons.org/licenses/by/4.0/
The gist: Data assimilation is a fundamental task in updating forecasting models upon observing new data, with applications ranging from weather prediction to online reinforcement learning.
Terminology
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.
Sources
- On Learnability under General Stochastic Processes
- Outlier-robust Kalman Filtering through Generalised Bayes
- Likelihood-free inference by ratio estimation
- AIFS-CRPS: Ensemble forecasting using a model trained with a loss function based on the Continuous Ranked Probability Score
- FourCastNet: A Global Data-driven High-resolution Weather Model using Adaptive Fourier Neural Operators
- GenCast: Diffusion-based ensemble forecasting for medium-range weather
- Generalized Bayesian deep reinforcement learning
- Proper scoring rules for estimation and forecast evaluation
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