Sequential Markov Chain Monte Carlo for Bayesian Filtering with Massive Data

TL;DR

This paper introduces two novel sequential MCMC algorithms designed for Bayesian filtering with massive datasets, significantly reducing computational costs while maintaining accuracy in non-linear, non-Gaussian models.

Contribution

The work develops two innovative Bayesian inference algorithms that efficiently handle large volumes of data through subsampling and divide-and-conquer strategies.

Findings

Achieves up to 90% computational savings compared to standard methods.

Maintains high accuracy in non-linear, non-Gaussian filtering tasks.

Demonstrates effectiveness through simulation results.

Abstract

Advances in digital sensors, digital data storage and communications have resulted in systems being capable of accumulating large collections of data. In the light of dealing with the challenges that massive data present, this work proposes solutions to inference and filtering problems within the Bayesian framework. Two novel Bayesian inference algorithms are developed for non-linear and non-Gaussian state space models, able to deal with large volumes of data (or observations). These are sequential Markov chain Monte Carlo (MCMC) approaches relying on two key ideas: 1) subsample the massive data and utilise a smaller subset for filtering and inference, and 2) a divide and conquer type approach computing local filtering distributions each using a subset of the measurements. Simulation results highlight the accuracy and the large computational savings, that can reach 90% by the proposed algorithms when compared with standard techniques.