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Bayesian Theory and Applications$
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Paul Damien, Petros Dellaportas, Nicholas G. Polson, and David A. Stephens

Print publication date: 2013

Print ISBN-13: 9780199695607

Published to Oxford Scholarship Online: May 2013

DOI: 10.1093/acprof:oso/9780199695607.001.0001

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Gibbs sampling for ordinary, robust and logistic regression with Laplace priors

Gibbs sampling for ordinary, robust and logistic regression with Laplace priors

Chapter:
(p.466) 23 Gibbs sampling for ordinary, robust and logistic regression with Laplace priors
Source:
Bayesian Theory and Applications
Author(s):

Robert B Gramacy

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199695607.003.0023

This chapter reviews the ideas behind the Gibbs samplers for both ordinary least squares (OLS) and logistic regression under regularization, focusing on the Laplace prior. The chapter is organized as follows. Section 23.2 considers OLS with extensions that allow for model selection and averaging, and heavy-tailed errors for robust estimation. Examples are provided using the implementation in the R package called monomvn, available on CRAN. Section 23.3 covers similar routines for logistic regression, with examples illustrated via the reglogit package. Section 23.4 concludes with references to further extensions to these methods.

Keywords:   Gibbs samplers, ordinary least squares, logistic regression, Laplace prior

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