Rossell, David and Telesca, Donatello (2017) Nonlocalpriors for high-dimensional estimation. Journal of the American Statistical Association, 112 (517). pp. 254-265. doi:10.1080/01621459.2015.1130634 ISSN 0162-1459.

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Abstract

Jointly achieving parsimony and good predictive power in high dimensions is a main challenge in statistics. Non-local priors (NLPs) possess appealing properties for model choice, but their use for estimation has not been studied in detail. We show that for regular models NLP-based Bayesian model averaging (BMA) shrink spurious parameters either at fast polynomial or quasi-exponential rates as the sample size n increases, while non-spurious parameter estimates are not shrunk. We extend some results to linear models with dimension p growing with n. Coupled with our theoretical investigations, we outline the constructive representation of NLPs as mixtures of truncated distributions that enables simple posterior sampling and extending NLPs beyond previous proposals. Our results show notable high-dimensional estimation for linear models with p > >n at low computational cost. NLPs provided lower estimation error than benchmark and hyper-g priors, SCAD and LASSO in simulations, and in gene expression data achieved higher cross-validated R2 with less predictors. Remarkably, these results were obtained without pre-screening variables. Our findings contribute to the debate of whether different priors should be used for estimation and model selection, showing that selection priors may actually be desirable for high-dimensional estimation.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics Q Science > QC Physics
Divisions:	Faculty of Science, Engineering and Medicine > Science > Statistics
Library of Congress Subject Headings (LCSH):	Markov processes, Monte Carlo method, Bayesian statistical decision theory
Journal or Publication Title:	Journal of the American Statistical Association
Publisher:	American Statistical Association
ISSN:	0162-1459
Official Date:	March 2017
Dates:	Date Event March 2017 Published 4 December 2015 Accepted 22 December 2015 Updated 10 December 2014 Submitted
Volume:	112
Number:	517
Page Range:	pp. 254-265
DOI:	10.1080/01621459.2015.1130634
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
Date of first compliant deposit:	17 December 2015
Date of first compliant Open Access:	22 June 2017
Funder:	National Institutes of Health (U.S.) (NIH)
Grant number:	R01 CA158113-01
Adapted As:

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