Griffin, J.E. and Brown, P.J. (2011) Bayesian hyper-lassos with non-convex penalization. Australian and New Zealand Journal of Statistics, 53 (4). pp. 423-442. ISSN 1369-1473 .
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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.
|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:||08 Jun 2012 11:14|
|Resource URI:||http://kar.kent.ac.uk/id/eprint/29598 (The current URI for this page, for reference purposes)|
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