English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

In this article we consider the estimation of the log-normalization constantassociated to a class of continuous-time filtering models. In particular, weconsider ensemble Kalman-Bucy filter based estimates based upon severalnonlinear Kalman-Bucy diffusions. Based upon new conditional bias results forthe mean of the afore-mentioned methods, we analyze the empirical log-scalenormalization constants in terms of their $\mathbb{L}_n-$errors and conditionalbias. Depending on the type of nonlinear Kalman-Bucy diffusion, we show thatthese 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 thetime horizon and $N$ is the ensemble size. Finally, we use these results foronline static parameter estimation for above filtering models and implement themethodology for both linear and nonlinear models.

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