TY - JOUR

T1 - Log-normalization constant estimation using the ensemble Kalman–Bucy filter with application to high-dimensional models

AU - Crisan, Dan

AU - Del Moral, Pierre

AU - Jasra, Ajay

AU - Ruzayqat, Hamza Mahmoud

N1 - KAUST Repository Item: Exported on 2022-10-06
Acknowledgements: A. J. and H. R. were supported by KAUST baseline funding. D. C. was partially supported by EU project STUOD—DLV-856408. We thank an editor and two referees for very useful comments which have greatly improved the paper.

PY - 2022/9/2

Y1 - 2022/9/2

N2 - 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 estimates based upon several nonlinear Kalman–Bucy diffusions. Using new conditional bias results for the mean of the aforementioned methods, we analyze the empirical log-scale normalization constants in terms of their -errors and -conditional bias. Depending on the type of nonlinear Kalman–Bucy diffusion, we show that these are bounded above by terms such as or (-errors) and or (-conditional bias), where t is the time horizon, N is the ensemble size, and is a constant that depends only on n, not on N or t. Finally, we use these results for online static parameter estimation for the above filtering models and implement the methodology for both linear and nonlinear models.

AB - 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 estimates based upon several nonlinear Kalman–Bucy diffusions. Using new conditional bias results for the mean of the aforementioned methods, we analyze the empirical log-scale normalization constants in terms of their -errors and -conditional bias. Depending on the type of nonlinear Kalman–Bucy diffusion, we show that these are bounded above by terms such as or (-errors) and or (-conditional bias), where t is the time horizon, N is the ensemble size, and is a constant that depends only on n, not on N or t. Finally, we use these results for online static parameter estimation for the above filtering models and implement the methodology for both linear and nonlinear models.

UR - http://hdl.handle.net/10754/667074

UR - https://www.cambridge.org/core/product/identifier/S0001867821000628/type/journal_article

U2 - 10.1017/apr.2021.62

DO - 10.1017/apr.2021.62

M3 - Article

SN - 0001-8678

SP - 1

EP - 25

JO - Advances in Applied Probability

JF - Advances in Applied Probability

ER -