Bayesian hyper-lassos with non-convex penalization

Griffin, Jim E. and Brown, Philip J. (2011) Bayesian hyper-lassos with non-convex penalization. Australian and New Zealand Journal of Statistics, 53 (4). pp. 423-442. ISSN 1369-1473 . (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided)

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The Lasso has sparked interest in the use of penalization of the log-likelihood for variable selection, as well as for shrinkage. We are particularly interested in the more-variables-thanobservations case of characteristic importance for modern data. The Bayesian interpretation of the Lasso as the maximum a posteriori estimate of the regression coefficients, which have been given independent, double exponential prior distributions, is adopted. Generalizing this prior provides a family of hyper-Lasso penalty functions, which includes the quasi-Cauchy distribution of Johnstone and Silverman as a special case. The properties of this approach, including the oracle property, are explored, and an EM algorithm for inference in regression problems is described. The posterior is multi-modal, and we suggest a strategy of using a set of perfectly fitting random starting values to explore modes in different regions of the parameter space. Simulations show that our procedure provides significant improvements on a range of established procedures, and we provide an example from chemometrics.

Item Type: Article
Uncontrolled keywords: Bayesian variable selection; hyper-Lasso; non-convexity; normal-exponential-gamma; oracle property; penalized likelihood
Subjects: Q Science > QA Mathematics (inc Computing science) > QA276 Mathematical statistics
Divisions: Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science > Statistics
Depositing User: Jim Griffin
Date Deposited: 30 May 2012 12:37
Last Modified: 13 May 2014 11:10
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