Unbiased estimation of the gradient of the log-likelihood for a class of continuous-time state-space models

Ballesio Marco () and Jasra Ajay ()
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Ballesio Marco: Computer, Electrical and Mathematical Sciences and Engineering Division, King Abdullah University of Science and Technology, Thuwal, 23955, Saudi Arabia
Jasra Ajay: Computer, Electrical and Mathematical Sciences and Engineering Division, King Abdullah University of Science and Technology, Thuwal, 23955, Saudi Arabia

Monte Carlo Methods and Applications, 2022, vol. 28, issue 1, 61-83

Abstract: In this paper, we consider static parameter estimation for a class of continuous-time state-space models. Our goal is to obtain an unbiased estimate of the gradient of the log-likelihood (score function), which is an estimate that is unbiased even if the stochastic processes involved in the model must be discretized in time. To achieve this goal, we apply a doubly randomized scheme, that involves a novel coupled conditional particle filter (CCPF) on the second level of randomization. Our novel estimate helps facilitate the application of gradient-based estimation algorithms, such as stochastic-gradient Langevin descent. We illustrate our methodology in the context of stochastic gradient descent (SGD) in several numerical examples and compare with the Rhee–Glynn estimator.

Keywords: Score function; particle filter; coupled conditional particle filter (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1515/mcma-2022-2105

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