Scalable Bayesian Inference for Time Series via Divide and Conquer

Rihui Ou, Lachlan Astfalck, Deborshee Sen, David Dunson

Journal of the American Statistical Association · Mon

DOI: 10.1080/01621459.2026.2688950

Abstract

Bayesian computation often scales poorly with increasing data size, motivating developments such as divide-and-conquer approaches for scalable inference. These methods partition the data into subsets, perform parallel inference on each subset, and aggregate the results into a single posterior. Appealing theoretical properties and practical performance have been demonstrated for independent data; however, methods for dependent data remain challenging. Existing methods rely on ad hoc approximations with limited theoretical guarantees that lead to potentially poor accuracy in practice. Here, we focus on time-series data and propose a simple, scalable divide-and-conquer method for dependent time series, with theoretically rigorous accuracy guarantees. Simulation studies and real-data examples are used to empirically verify the effectiveness of our approach. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.

Keywords

Dependent data, Embarrassingly parallel, Markov chain Monte Carlo, Scalable Bayes, Wasserstein barycenter

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