Spectral divide-and-conquer MCMC for long stationary time series

2026-09-20

AI Summary

本文提出了一种基于频域的并行MCMC方法，解决了长时间序列模型中的计算瓶颈问题，通过分布式快速傅里叶变换和并行计算框架提高了贝叶斯推断的可扩展性。

Abstract

The temporal dependence inherent in time series models poses a fundamental challenge for distributed Bayesian inference, as it precludes embarrassingly parallel algorithms based on naive independence assumptions in the time domain. We propose a frequency-domain framework for scalable Bayesian inference in stationary time series that exploits the asymptotic independence underlying the Whittle likelihood. To exploit parallel computing resources, we develop a distributed fast Fourier transform and integrate it with embarrassingly parallel Markov chain Monte Carlo (MCMC) algorithms within a modern cluster-computing framework. This enables the analysis of time series that exceed the memory capacity of a single computational node or for which computation time is a bottleneck. The proposed methodology is compatible with a broad class of existing divide-and-conquer algorithms for independent data by applying them to frequency-domain rather than time-domain partitions. We establish that the error of the spectral divide-and-conquer MCMC posterior approximation relative to the exact time-domain posterior converges to zero in probability in a shrinking neighbourhood of the full-data Whittle posterior mode. The corresponding convergence rate is also derived. Across several experiments, we demonstrate that our approach provides accurate approximations to the full-data Whittle posterior. The proposed method is shown to outperform the current state-of-the-art time-domain divide-and-conquer methodology, particularly for highly persistent processes. The methodology is further illustrated by fitting a semi-long range model to a long meteorological time series.

Problem

• temporal dependence
• distributed Bayesian inference
• stationary time series

Innovation

• Spectral divide-and-conquer MCMC
• Distributed Fast Fourier Transform
• Whittle likelihood
• Scalable Bayesian inference