A Bayesian binary regression model with exponential power link

A flexible Bayesian approach of a generalized linear model is proposed to describe the depen-dence of binary data on explanatory variables. The inverse exponential power cumulative distributionfunction is used as the link of the binary regression model. The power exponential family providesdistributions with both lighter and heavier tails compared to the normal one, and includes the normaland an approximation to the logistic distribution as particular cases. The idea of using a data aug-mentation framework and a mixture representation of the power exponential distribution is exploitedto derive efficient Gibbs sampling algorithms for both informative and non informative settings. Anexample illustrate the performance of the proposed approach when comparing with other competingmodels.Int. Statistical Inst.: Proc. 58th World Statistical Congress, 2011, Dublin (Session CPS027)p.6516