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

2 CQFD - Quality control and dynamic reliability
IMB - Institut de Mathématiques de Bordeaux, Inria Bordeaux - Sud-Ouest
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.
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Preprints, Working Papers, ...
Domain :

https://hal.inria.fr/hal-03131613
Contributor : Pierre del Moral Connect in order to contact the contributor
Submitted on : Thursday, February 4, 2021 - 2:59:59 PM
Last modification on : Friday, January 21, 2022 - 3:22:55 AM

### Identifiers

• HAL Id : hal-03131613, version 1
• ARXIV : 2101.11460

### Citation

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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