We develop an extension of the classical Zellner's g-prior to generalized
linear models. Any continuous proper hyperprior f(g) can be used, giving rise
to a large class of hyper-g priors. Connections with the literature are described
in detail. A fast and accurate integrated Laplace approximation of the marginal
likelihood makes inference in large model spaces feasible. For posterior parameter
estimation we propose an ecient and tuning-free Metropolis-Hastings sampler.
The methodology is illustrated with variable selection and automatic covariate
transformation in the Pima Indians diabetes data set.