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Activity Number:
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165
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Type:
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Invited
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Date/Time:
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Monday, August 4, 2008 : 2:00 PM to 3:50 PM
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Sponsor:
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Section on Nonparametric Statistics
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| Abstract - #300111 |
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Title:
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Bayesian Smoothness and Shrinkage Priors in Regression
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Author(s):
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Ludwig Fahrmeir*+ and Thomas Kneib
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Companies:
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University of Munich and University of Munich
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Address:
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Ludwig-Maximilians-University, Munich, International, D-81375, Germany
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Keywords:
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Bayesian regularisation ; hierarchical models ; high-dimensional data ; non-Gaussian ridge regression ; scale mixtures of normals
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Abstract:
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We present a Bayesian approach to generalized regression situations that combines smoothing of nonparametric functions and spatial effects based on smoothness priors with regularization of high-dimensional covariate effects based on shrinkage priors. A general class of smoothing priors is given by multivariate correlated Gaussian distributions, where the precision matrix determines smoothness based on adjacency information. Shrinkage priors are obtained by considering i.i.d. priors with i.i.d. Gaussian priors corresponding to ridge regression as the simplest example. A hierarchical formulation of (scale) mixtures of normals or mixtures of smoothing variances yields a comprehensive class of priors that includes the LASSO as a special case. Due to the hierarchical formulation, existing MCMC algorithms can be adapted with only slight modifications.
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