Hierarchical Bayesian semiparametric procedures for logistic regression

SUMMARY A simple procedure is proposed for exact computation to smooth Bayesian estimates for logistic regression functions, when these are not constrained to lie on a fitted regression surface. Exact finite sample inferences and predictions are available, together with an exact residual analysis. The prior distribution relates to O'Hagan's assumptions for a normal regression function. A global shrinkage parameter and local smoothness parameter can be evaluated from the current data by hierarchical Bayesian procedures. Consideration of the shrinkage parameter permits an overall check regarding a hypothesised regression model. No optimisation technique is needed, since Monte Carlo simulations from independent logistic distributions can be directly employed. The complexity of the computations does not substantively increase with the dimensionality of the design space.