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

The Inverse-Wishart (IW) distribution is a standard and popular choice ofpriors for covariance matrices and has attractive properties such asconditional conjugacy. However, the IW family of priors has crucial drawbacks,including the lack of effective choices for non-informative priors. Severalclasses of priors for covariance matrices that alleviate these drawbacks, whilepreserving computational tractability, have been proposed in the literature.These priors can be obtained through appropriate scale mixtures of IW priors.However, in the era of increasing dimensionality, the posterior consistency ofmodels that incorporate such priors has not been investigated. We address thisissue for the multi-response regression setting ($q$ responses, $n$ samples)under a wide variety of IW scale mixture priors for the error covariancematrix. Posterior consistency and contraction rates for both the regressioncoefficient matrix and the error covariance matrix are established in the``large $q$, large $n$'' setting under mild assumptions on the truedata-generating covariance matrix and relevant hyperparameters. In particular,the number of responses $q_n$ is allowed to grow with $n$, but with $q_n =o(n)$. Also, some results related to the inconsistency of the posteriordistribution and posterior mean for $q_n/n \to \gamma$, where $\gamma \in(0,\infty)$ are provided.

Posterior consistency in multi-response regression models with non-informative priors for the error covariance matrix in growing dimensions