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 Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We show that lower-dimensional marginal densities of dependent zero-meannormal distributions truncated to the positive orthant exhibit a mass-shiftingphenomenon. Despite the truncated multivariate normal density having a mode atthe origin, the marginal density assigns increasingly small mass near theorigin as the dimension increases. The phenomenon accentuates with strongercorrelation between the random variables. A precise quantificationcharacterizing the role of the dimension as well as the dependence is provided.This surprising behavior has serious implications towards Bayesian constrainedestimation and inference, where the prior, in addition to having a fullsupport, is required to assign a substantial probability near the origin tocapture at parts of the true function of interest. Without furthermodification, we show that truncated normal priors are not suitable formodeling at regions and propose a novel alternative strategy based on shrinkingthe coordinates using a multiplicative scale parameter. The proposed shrinkageprior is empirically shown to guard against the mass shifting phenomenon whileretaining computational efficiency.

Mass-shifting phenomenon of truncated multivariate normal priors