Bayesian semiparametric symmetric models for binary data

Abstract

This work proposes a general Bayesian semiparametric model for binary data. Symmetric prior probability curves as an extension for discussed ideas from Basu and Mukhopadhyay (Generalized Linear Models:ABayesian Perspective, pp. 231–241, 1998) are considered using the blocked Gibbs sampler, which is more general than the Polya urn Gibbs sampler. The Bayesian semiparametric approach allows us to incorporate uncertainty around the F distribution of the latent data and to model heavy-tailed or light-tailed distributions. In particular, the Bayesian semiparametric logistic model is introduced, which enables one to elicit prior distributions for regression coefficients from information about odds ratios; this is quite interesting in applied research. Then, this framework opens several possibilities to deal with binary data in the Bayesian perspective.