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