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Hierarchical Models

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Bayesian Nonparametric Data Analysis

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

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Abstract

One of the great success stories of Bayesian methods in biostatistics is inference in hierarchical models. The model-based Bayesian approach allows for coherent propagation of uncertainties and borrowing of strength across submodels and more. In this chapter we discuss nonparametric Bayesian approaches in hierarchical models, including nonparametric priors on random effects distributions and extensions of such models across multiple related studies. Honest accounting for uncertainties becomes particularly important for applications to classification, when we use posterior predictive inference for a future experimental unit to estimate unknown membership in one of several subpopulations.

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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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Müller, P., Quintana, F.A., Jara, A., Hanson, T. (2015). Hierarchical Models. In: Bayesian Nonparametric Data Analysis. Springer Series in Statistics. Springer, Cham. https://doi.org/10.1007/978-3-319-18968-0_7

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