Bayesian Inference for Semiparametric Binary Regression

Abstract

We propose a regression model for binary response data that 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. We design a Markov chain Monte Carlo algorithm for posterior simulation and apply the methodology to data on radiotherapy treatments for cancer.

Key Words:

• Dirichlet process
• Latent variables
• Link function
• Logistic regression
• Markov chain Monte Carlo
• Polya sequence