A General-Purpose Fixed-Lag No-U-Turn Sampler for Nonlinear Non-Gaussian State Space Models

Particle Filters (PFs) are commonly used Sequential Monte Carlo (SMC) algorithms to process a never-ending stream of measurements relating to a nonlinear non-Gaussian state space model. Fixed-Lag SMC (FL-SMC) is an extension to the PF that allows for re-processing of historic data. FL-SMC is widely flexible, such that it can solve problems that are challenging for standard PFs. However, FL-SMC also inherits the challenges (in terms of maximizing accuracy and efficiency) that can limit PFs' efficacy when using a poor choice of the proposal distribution: this can be especially evident in strongly nonlinear scenarios. One alternative is to employ Sequential Markov Chain Monte Carlo (S-MCMC) methods, for which the literature offers a wider selection of efficient proposal distributions. However, S-MCMC does not inherently have the broad applicability of FL-SMC. In this paper, we present the Fixed-Lag No-U-Turn Sampler, an SMC framework that combines FL-SMC and No-U-Turn Sampler (NUTS), a gradient-based MCMC method. We show that, when compared with several variants of PFs, including one that employs Particle Flow, several variants of FL-SMC, and S-MCMC, our proposed approach provides significant accuracy and efficiency improvements, at the price of a moderate run-time overhead.