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Regression

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Bayesian Nonparametric Data Analysis

Part of the book series: Springer Series in Statistics ((SSS))

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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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Authors and Affiliations

  1. Department of Mathematics, University of Texas at Austin, Austin, TX, USA

    Peter Müller

  2. Departamento de Estadística, Pontificia Universidad Católica, Santiago, Chile

    Fernando Andrés Quintana & Alejandro Jara

  3. Department of Statistics, University of South Carolina, Columbia, SC, USA

    Tim Hanson

Authors
  1. Peter Müller
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  2. Fernando Andrés Quintana
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  3. Alejandro Jara
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  4. Tim Hanson
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© 2015 Springer International Publishing Switzerland

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Müller, P., Quintana, F.A., Jara, A., Hanson, T. (2015). Regression. In: Bayesian Nonparametric Data Analysis. Springer Series in Statistics. Springer, Cham. https://doi.org/10.1007/978-3-319-18968-0_4

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