Stochastic Gradient MCMC for Nonlinear State Space Models

Aicher, Christopher and Putcha, Srshti and Nemeth, Christopher and Fearnhead, Paul and Fox, Emily B. (2023) Stochastic Gradient MCMC for Nonlinear State Space Models. Bayesian Analysis. ISSN 1936-0975 (In Press)

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Abstract

State space models (SSMs) provide a exible 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  lters additionally su er from increasing particle degeneracy with longer series. Stochastic gradient MCMC methods have been developed to scale Bayesian inference for  nite-state hidden Markov models and linear SSMs using bu ered 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 bu ering error and particle error in the case of nonlinear SSMs that are log-concave in the latent process. We evaluate our proposed particle bu ered stochastic gradient using stochastic gradient MCMC for inference on both long sequential synthetic and minute-resolution  nancial returns data, demonstrating the importance of this class of methods.