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2015 | OriginalPaper | Buchkapitel

4. Regression

verfasst von : Peter Müller, Fernando Andrés Quintana, Alejandro Jara, Tim Hanson

Erschienen in: Bayesian Nonparametric Data Analysis

Verlag: Springer International Publishing

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Abstract

Regression problems naturally call for nonparametric Bayesian methods when one wishes to relax restrictive parametric assumptions on the mean function, the residual distribution or both. We introduce suitable nonparametric Bayesian methods to facilitate such generalizations, including priors for random mean functions, the use of nonparametric density estimation for residual distributions and finally nonparametric Bayesian methods for fully nonparametric regression when both mean function and residual distribution are modeled nonparametrically. The latter includes approaches where the complete shape of the response distribution is allowed to change as a function of the predictors, which is also known as density regression. We introduce the popular dependent Dirichlet process model and several other alternatives.

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Vorheriges Kapitel Density Estimation: Models Beyond the DP

Nächstes Kapitel Categorical Data

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Titel: Regression
verfasst von: Peter Müller
Fernando Andrés Quintana
Alejandro Jara
Tim Hanson
Verlag: Springer International Publishing
Buch: Bayesian Nonparametric Data Analysis
Print ISBN: 978-3-319-18967-3

Electronic ISBN: 978-3-319-18968-0

Copyright-Jahr: 2015
DOI: https://doi.org/10.1007/978-3-319-18968-0_4

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