Likelihood Subgradient Densities

We introduce likelihood subgradient densities and explore their basic properties. Using mixtures of likelihood subgradient densities, we propose an approach for constructing tight enveloping functions in the Bayesian context. In the case of normal priors with normal data, the area underneath the resulting enveloping function is bounded above by . The approach is extended to k-dimensional models where the corresponding bound is . More generally, our approach should also yield tight enveloping functions for other models in which the data are close to normal. Such models include generalized linear models (e.g., Bayesian Poisson regression and the Bayesian logit model). Simulations based on the approach are performed for two separate models using accept-reject methods.