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

Dan Crisan
• Function : Author
Pierre del Moral
Ajay Jasra
• Function : Author
Hamza Ruzayqat
• Function : Author

#### 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.

#### Domains

Mathematics [math] Probability [math.PR]

### Dates and versions

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

### Identifiers

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

### Cite

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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