Log-Normalization Constant Estimation using the Ensemble Kalman-Bucy Filter with Application to High-Dimensional Models
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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 𝕃_n-errors and conditional bias. Depending on the type of nonlinear Kalman-Bucy diffusion, we show that these are of order (√(t/N)) + t/N or 1/√(N) (𝕃_n-errors) and of order [t+√(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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