A DIFFUSE PRIOR LIMIT IN SEMIPARAMETRIC BINARY REGRESSION

A DIFFUSE PRIOR LIMIT IN SEMIPARAMETRIC BINARY REGRESSION

Michael A. Newton

1994 American Statistical Association Proceedings of the Section on Bayesian Statistical Science 181--186

Also, Technical Report 936, Department of Statistics, University of Wisconsin, Madison.

Abstract:

We place a standard Dirichlet process prior on the inverse-link function of a binary regression model and study the posterior distribution as the prior precision parameter converges to zero. Simple closed-form expressions are available for the limiting posterior density of the regression parameters and the posterior predictive distribution. This limiting posterior exhibits instability as the sample size grows and does not generally produce consistent estimators. A more stable variation of the Dirichlet process prior is also discussed.

Keywords: Dirichlet process, Polya sequence, logistic regression, link function


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