A DIFFUSE PRIOR LIMIT IN SEMIPARAMETRIC BINARY REGRESSION

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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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