Mameli, Valentina;
Slanzi, Debora;
Griffin, Jim E;
Brown, Philip J;
(2025)
Multivariate Bayesian Global–Local Shrinkage Methods for Regularisation in the High-Dimensional Linear Model.
Mathematics
, 13
(11)
, Article 1812. 10.3390/math13111812.
Preview |
PDF
mathematics-13-01812.pdf - Published Version Download (363kB) | Preview |
Abstract
This paper considers Bayesian regularisation using global–local shrinkage priors in the multivariate general linear model when there are many more explanatory variables than observations. We adopt priors’ structures used extensively in univariate problems (conjugate and non-conjugate with tail behaviour ranging from polynomial to exponential) and consider how the addition of error correlation in the multivariate set-up affects the performance of these priors. Two different datasets (from drug discovery and chemometrics) with many covariates are used for comparison, and these are supplemented by a small simulation study to corroborate the role of error correlation. We find that structural assumptions of the prior distribution on regression coefficients can be more significant than the tail behaviour. In particular, if the structural assumption of conjugacy is used, the performance of the posterior predictive distribution deteriorates relative to non-conjugate choices as the error correlation becomes stronger.
| Type: | Article |
|---|---|
| Title: | Multivariate Bayesian Global–Local Shrinkage Methods for Regularisation in the High-Dimensional Linear Model |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.3390/math13111812 |
| Publisher version: | https://doi.org/10.3390/math13111812 |
| Language: | English |
| Additional information: | This work is licensed under a Creative Commons License. The images or other third-party material in this article are included in the Creative Commons license, unless indicated otherwise in the credit line; if the material is not included under the Creative Commons license, users will need to obtain permission from the license holder to reproduce the material. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/ |
| Keywords: | Seemingly unrelated multivariate normal regression; structured priors; global– local priors; exponential-tailed and polynomial-tailed priors; drug discovery; chemometrics; MSC: 62F15; 62H12; 62J07 |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Statistical Science |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10209426 |
Archive Staff Only
 |
View Item |
