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/

Global: Zendy Tools annual

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

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

The posterior covariance matrix W defined by the log-likelihood of eachobservation plays important roles both in the sensitivity analysis andfrequencist's evaluation of the Bayesian estimators. This study focused on thematrix W and its principal space; we term the latter as an essential subspace.First, it is shown that they appear in various statistical settings, such asthe evaluation of the posterior sensitivity, assessment of the frequencist'suncertainty from posterior samples, and stochastic expansion of the loss; a keytool to treat frequencist's properties is the recently proposed Bayesianinfinitesimal jackknife approximation (Giordano and Broderick (2023)). In thefollowing part, we show that the matrix W can be interpreted as a reproducingkernel; it is named as W-kernel. Using the W-kernel, the essential subspace isexpressed as a principal space given by the kernel PCA. A relation to theFisher kernel and neural tangent kernel is established, which elucidates theconnection to the classical asymptotic theory; it also leads to a sort ofBayesian-frequencist's duality. Finally, two applications, selection of arepresentative set of observations and dimensional reduction in the approximatebootstrap, are discussed. In the former, incomplete Cholesky decomposition isintroduced as an efficient method to compute the essential subspace. In thelatter, different implementations of the approximate bootstrap for posteriormeans are compared.

W-kernel and essential subspace for frequencist's evaluation of Bayesian estimators