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The New England Journal of Statistics in Data Science


Bayesian Simultaneous Partial Envelope Model with Application to an Imaging Genetics Analysis
Volume 1, Issue 2 (2023), pp. 237–269
Pub. online: 2 February 2023      Type: Statistical Methodology      Open accessOpen Access
Accepted
4 January 2023
Published
2 February 2023

Abstract

As a prominent dimension reduction method for multivariate linear regression, the envelope model has received increased attention over the past decade due to its modeling flexibility and success in enhancing estimation and prediction efficiencies. Several enveloping approaches have been proposed in the literature; among these, the partial response envelope model [57] that focuses on only enveloping the coefficients for predictors of interest, and the simultaneous envelope model [14] that combines the predictor and the response envelope models within a unified modeling framework, are noteworthy. In this article we incorporate these two approaches within a Bayesian framework, and propose a novel Bayesian simultaneous partial envelope model that generalizes and addresses some limitations of the two approaches. Our method offers the flexibility of incorporating prior information if available, and aids coherent quantification of all modeling uncertainty through the posterior distribution of model parameters. A block Metropolis-within-Gibbs algorithm for Markov chain Monte Carlo (MCMC) sampling from the posterior is developed. The utility of our model is corroborated by theoretical results, comprehensive simulations, and a real imaging genetics data application for the Alzheimer’s Disease Neuroimaging Initiative (ADNI) study.

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© 2023 New England Statistical Society
Open access article under the CC BY license.

Keywords
Bayesian envelope model Multivariate regression Reducing subspace Simultaneous envelope Partial envelope Imaging genetics

Funding
C. Zhang’s work was partially supported by U.S. National Science Foundation grants DMS-2013486 and DMS-1712418, and provided by the University of Wisconsin-Madison Office of the Vice Chancellor for Research and Graduate Education with funding from the Wisconsin Alumni Research Foundation. Park’s research is partially supported by University of Wisconsin-Madison Office of the Vice Chancellor for Research and Graduate Education. Data collection and sharing for this project was funded by the Alzheimer’s Disease Neuroimaging Initiative (ADNI) (National Institutes of Health Grant U01 AG024904) and DOD ADNI (Department of Defense award number W81XWH-12-2-0012). ADNI is funded by the National Institute on Aging, the National Institute of Biomedical Imaging and Bioengineering, and through generous contributions from the following: AbbVie, Alzheimer’s Association; Alzheimer’s Drug Discovery Foundation; Araclon Biotech; BioClinica, Inc.; Biogen; Bristol-Myers Squibb Company; CereSpir, Inc.; Cogstate; Eisai Inc.; Elan Pharmaceuticals, Inc.; Eli Lilly and Company; EuroImmun; F. Hoffmann-La Roche Ltd and its affiliated company Genentech, Inc.; Fujirebio; GE Healthcare; IXICO Ltd.; Janssen Alzheimer Immunotherapy Research & Development, LLC.; Johnson & Johnson Pharmaceutical Research & Development LLC.; Lumosity; Lundbeck; Merck & Co., Inc.; Meso Scale Diagnostics, LLC.; NeuroRx Research; Neurotrack Technologies; Novartis Pharmaceuticals Corporation; Pfizer Inc.; Piramal Imaging; Servier; Takeda Pharmaceutical Company; and Transition Therapeutics. The Canadian Institutes of Health Research is providing funds to support ADNI clinical sites in Canada. Private sector contributions are facilitated by the Foundation for the National Institutes of Health (www.fnih.org). The grantee organization is the Northern California Institute for Research and Education, and the study is coordinated by the Alzheimer’s Therapeutic Research Institute at the University of Southern California. ADNI data are disseminated by the Laboratory for Neuro Imaging at the University of Southern California.

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