# Prequential posteriors

arXiv: https://arxiv.org/abs/2511.17721 · HTML: https://mlsanity.com/paper/2511.17721/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 68 references that are in the map.
- First posted on arXiv 21 Nov 2025.

## Builds on (most cited first, 21 of 21)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [FourCastNet: A Global Data-driven High-resolution Weather Model using Adaptive Fourier Neural Operators](https://mlsanity.com/paper/2202.11214/) (2022)
- [Stochastic Gradient Hamiltonian Monte Carlo](https://mlsanity.com/paper/1402.4102/) (2014)
- [ClimaX: A foundation model for weather and climate](https://mlsanity.com/paper/2301.10343/) (2023)
- [WeatherBench: A benchmark dataset for data-driven weather forecasting](https://mlsanity.com/paper/2002.00469/) (2020)
- [GenCast: Diffusion-based ensemble forecasting for medium-range weather](https://mlsanity.com/paper/2312.15796/) (2023)
- [A General Framework for Updating Belief Distributions](https://mlsanity.com/paper/1306.6430/) (2013)
- [Pangu-Weather: A 3D High-Resolution Model for Fast and Accurate Global Weather Forecast](https://mlsanity.com/paper/2211.02556/) (2022)
- [Likelihood-free inference by ratio estimation](https://mlsanity.com/paper/1611.10242/) (2016)
- [Probabilistic Forecasting with Generative Networks via Scoring Rule Minimization](https://mlsanity.com/paper/2112.08217/) (2021)
- [Approximate Bayesian computation with the Wasserstein distance](https://mlsanity.com/paper/1905.03747/) (2019)
- [Bayesian Synthetic Likelihood](https://mlsanity.com/paper/2305.05120/) (2023)
- [Deep Generative Data Assimilation in Multimodal Setting](https://mlsanity.com/paper/2404.06665/) (2024)
- [Outlier-robust Kalman Filtering through Generalised Bayes](https://mlsanity.com/paper/2405.05646/) (2024)
- [Proper scoring rules for estimation and forecast evaluation](https://mlsanity.com/paper/2504.01781/) (2025)
- [Bridging the Gap between Stochastic Gradient MCMC and Stochastic Optimization](https://mlsanity.com/paper/1512.07962/) (2015)
- [The Ensemble Kalman Filter: A Signal Processing Perspective](https://mlsanity.com/paper/1702.08061/) (2017)
- [Digital Twins: State of the Art Theory and Practice, Challenges, and Open Research Questions](https://mlsanity.com/paper/2011.02833/) (2020)
- [Generalized Bayesian Likelihood-Free Inference](https://mlsanity.com/paper/2104.03889/) (2021)
- [Robust Bayesian Synthetic Likelihood via a Semi-Parametric Approach](https://mlsanity.com/paper/1809.05800/) (2018)
- [Generalized Bayesian deep reinforcement learning](https://mlsanity.com/paper/2412.11743/) (2024)

## Abstract (arXiv)

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.