Bayesian inference for semiparametric binary regression

### 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.