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December 2015 A Fully Nonparametric Modeling Approach to Binary Regression
Maria DeYoreo, Athanasios Kottas
Bayesian Anal. 10(4): 821-847 (December 2015). DOI: 10.1214/15-BA963SI

Abstract

We propose a general nonparametric Bayesian framework for binary regression, which is built from modeling for the joint response–covariate distribution. The observed binary responses are assumed to arise from underlying continuous random variables through discretization, and we model the joint distribution of these latent responses and the covariates using a Dirichlet process mixture of multivariate normals. We show that the kernel of the induced mixture model for the observed data is identifiable upon a restriction on the latent variables. To allow for appropriate dependence structure while facilitating identifiability, we use a square-root-free Cholesky decomposition of the covariance matrix in the normal mixture kernel. In addition to allowing for the necessary restriction, this modeling strategy provides substantial simplifications in implementation of Markov chain Monte Carlo posterior simulation. We present two data examples taken from areas for which the methodology is especially well suited. In particular, the first example involves estimation of relationships between environmental variables, and the second develops inference for natural selection surfaces in evolutionary biology. Finally, we discuss extensions to regression settings with ordinal responses.

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Maria DeYoreo. Athanasios Kottas. "A Fully Nonparametric Modeling Approach to Binary Regression." Bayesian Anal. 10 (4) 821 - 847, December 2015. https://doi.org/10.1214/15-BA963SI

Information

Published: December 2015
First available in Project Euclid: 17 July 2015

zbMATH: 1334.62035
MathSciNet: MR3432241
Digital Object Identifier: 10.1214/15-BA963SI

Rights: Copyright © 2015 International Society for Bayesian Analysis

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Vol.10 • No. 4 • December 2015
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