CRISAN, Dan; DEL MORAL, Pierre; JASRA, Ajay; RUZAYQAT, Hamza

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CRISAN, Dan
Imperial College London

DEL MORAL, Pierre
Quality control and dynamic reliability [CQFD]

JASRA, Ajay
King Abdullah University of Science and Technology [Saudi Arabia] [KAUST]

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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.< Réduire

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Kalman-Bucy filter

Riccati equations

Nonlinear Markov processes

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

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