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 Plus annual

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

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Let $X| \mu \sim N_p(\mu,v_xI)$ and $Y| \mu \sim N_p(\mu,v_yI)$ beindependent p-dimensional multivariate normal vectors with common unknown mean$\mu$. Based on only observing $X=x$, we consider the problem of obtaining apredictive density $\hat{p}(y| x)$ for $Y$ that is close to $p(y| \mu)$ asmeasured by expected Kullback--Leibler loss. A natural procedure for thisproblem is the (formal) Bayes predictive density $\hat{p}_{\mathrm{U}}(y| x)$under the uniform prior $\pi_{\mathrm{U}}(\mu)\equiv 1$, which is bestinvariant and minimax. We show that any Bayes predictive density will beminimax if it is obtained by a prior yielding a marginal that is superharmonicor whose square root is superharmonic. This yields wide classes of minimaxprocedures that dominate $\hat{p}_{\mathrm{U}}(y| x)$, including Bayespredictive densities under superharmonic priors. Fundamental similarities anddifferences with the parallel theory of estimating a multivariate normal meanunder quadratic loss are described.

Improved minimax predictive densities under Kullback–Leibler loss