Bayesian inference for semiparametric binary regression

Michael A. Newton , Claudia Czado and Rick Chappell

1996 Journal of the American Statistical Association, 91, 142-153.

Formerly, Technical Report 905, Department of Statistics, University of Wisconsin, Madison.

Abstract:

We propose a regression model for binary response data which places no structural restrictions on the link function except monotonicity and known location and scale. Predictors enter linearly. We demonstrate Bayesian inference calculations in this model. By modifying the Dirichlet process, we obtain a natural prior measure over this semiparametric model, and we use Polya sequence theory to formulate this measure in terms of a finite number of unobserved variables. A Markov chain Monte Carlo algorithm is designed for posterior simulation, and the methodology is applied to data on radiotherapy treatments for cancer.

Keywords: Dirichlet process, Polya sequence, logistic regression, Markov chain Monte Carlo, latent variables, link function

Contact Michael A. Newton for a reprint, or for computer code.