High-dimensional Filtering using Nested Sequential Monte Carlo
This addresses a bottleneck in Bayesian filtering for high-dimensional models, enabling more efficient inference in domains like spatio-temporal analysis.
The paper tackles the challenge of Sequential Monte Carlo (SMC) methods struggling in high dimensions by proposing nested sequential Monte Carlo (NSMC), which generalizes SMC to allow approximate samples from proposals while maintaining correctness, resulting in improved accuracy on spatio-temporal state space models.
Sequential Monte Carlo (SMC) methods comprise one of the most successful approaches to approximate Bayesian filtering. However, SMC without good proposal distributions struggle in high dimensions. We propose nested sequential Monte Carlo (NSMC), a methodology that generalises the SMC framework by requiring only approximate, properly weighted, samples from the SMC proposal distribution, while still resulting in a correct SMC algorithm. This way we can exactly approximate the locally optimal proposal, and extend the class of models for which we can perform efficient inference using SMC. We show improved accuracy over other state-of-the-art methods on several spatio-temporal state space models.