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Preprints, Working Papers, ... Year : 2021

Log-Normalization Constant Estimation using the Ensemble Kalman-Bucy Filter with Application to High-Dimensional Models

Abstract

In this article we consider the estimation of the log-normalization constant associated to a class of continuous-time filtering models. In particular, we consider ensemble Kalman-Bucy filter based estimates based upon several nonlinear Kalman-Bucy diffusions. Based upon new conditional bias results for the mean of the afore-mentioned methods, we analyze the empirical log-scale normalization constants in terms of their $\mathbb{L}_n-$errors and conditional bias. Depending on the type of nonlinear Kalman-Bucy diffusion, we show that these are of order $(\sqrt{t/N}) + t/N$ or $1/\sqrt{N}$ ($\mathbb{L}_n-$errors) and of order $[t+\sqrt{t}]/N$ or $1/N$ (conditional bias), where $t$ is the time horizon and $N$ is the ensemble size. Finally, we use these results for online static parameter estimation for above filtering models and implement the methodology for both linear and nonlinear models.

Dates and versions

hal-03131613 , version 1 (04-02-2021)

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Dan Crisan, Pierre del Moral, Ajay Jasra, Hamza Ruzayqat. Log-Normalization Constant Estimation using the Ensemble Kalman-Bucy Filter with Application to High-Dimensional Models. 2021. ⟨hal-03131613⟩
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