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2023 Stochastic Gradient MCMC for Nonlinear State Space Models
Christopher Aicher, Srshti Putcha, Christopher Nemeth, Paul Fearnhead, Emily Fox
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Bayesian Anal. Advance Publication 1-23 (2023). DOI: 10.1214/23-BA1395


State space models (SSMs) provide a flexible framework for modeling complex time series via a latent stochastic process. Inference for nonlinear, non-Gaussian SSMs is often tackled with particle methods that do not scale well to long time series. The challenge is two-fold: not only do computations scale linearly with time, as in the linear case, but particle filters additionally suffer from increasing particle degeneracy with longer series. Stochastic gradient MCMC methods have been developed to scale Bayesian inference for finite-state hidden Markov models and linear SSMs using buffered stochastic gradient estimates to account for temporal dependencies. We extend these stochastic gradient estimators to nonlinear SSMs using particle methods. We present error bounds that account for both buffering error and particle error in the case of nonlinear SSMs that are log-concave in the latent process. We evaluate our proposed particle buffered stochastic gradient using stochastic gradient MCMC for inference on both long sequential synthetic and minute-resolution financial returns data, demonstrating the importance of this class of methods.

Funding Statement

This work was supported in part by: ONR Grants N00014-15-1-2380, N00014-18-1-2862, and N00014-22-1-2110; NSF CAREER Award IIS-1350133; AFOSR Grant FA9550-21-1-0397; and, EPSRC Grants EP/L015692/1, EP/S00159X/1, EP/V022636/1, EP/R01860X/1, EP/R018561/1 and EP/R034710/1.


We would like to thank Nicholas Foti for helpful discussions.


Download Citation

Christopher Aicher. Srshti Putcha. Christopher Nemeth. Paul Fearnhead. Emily Fox. "Stochastic Gradient MCMC for Nonlinear State Space Models." Bayesian Anal. Advance Publication 1 - 23, 2023.


Published: 2023
First available in Project Euclid: 11 July 2023

Digital Object Identifier: 10.1214/23-BA1395

Keywords: Bayesian inference , exponential forgetting , Markov chain Monte Carlo , nonlinear state space model , particle filtering , stochastic gradient

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