Alternative prior distributions for variable selection with very many more variables than observations
Griffin, Jim E. and Brown, Philip J. (2005) Alternative prior distributions for variable selection with very many more variables than observations. Working Paper. Coventry: University of Warwick. Centre for Research in Statistical Methodology. Working papers, Vol.2005 (No.10).
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Official URL: http://www2.warwick.ac.uk/fac/sci/statistics/crism...
The problem of variable selection in regression and the generalised linear model is addressed.
We adopt a Bayesian approach with priors for the regression coefficients that are
scale mixtures of normal distributions and embody a high prior probability of proximity to
zero. By seeking modal estimates we generalise the lasso. Properties of the priors and their
resultant posteriors are explored in the context of the linear and generalised linear model especially
when there are more variables than observations. We develop EM algorithms that
embrace the need to explore the multiple modes of the non log-concave posterior distributions.
Finally we apply the technique to microarray data using a probit model to find the
genetic predictors of osteo- versus rheumatoid arthritis.
Keywords: Bayesian modal analysis, Variable selection in regression, Scale mixtures of
normals, Improper Jeffreys prior, lasso, Penalised likelihood, EMalgorithm, Multiple modes,
More variables than observations, Singular value decomposition, Latent variables, Probit
|Item Type:||Working or Discussion Paper (Working Paper)|
|Subjects:||Q Science > QA Mathematics|
|Divisions:||Faculty of Science > Statistics|
|Library of Congress Subject Headings (LCSH):||Regression analysis, Mixture distributions (Probability theory)|
|Series Name:||Working papers|
|Publisher:||University of Warwick. Centre for Research in Statistical Methodology|
|Place of Publication:||Coventry|
|Number of Pages:||34|
|Status:||Not Peer Reviewed|
|Access rights to Published version:||Open Access|
|Funder:||Commonwealth Scientific and Industrial Research Organization (Australia) (CSIRO)|
Abramowitz, M. and Stegun, I. A. (Eds.) (1964) “Handbook of Mathematical Functions
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