Integrated objective Bayesian estimation and hypothesis testing

The complete final product of Bayesian inference is the posterior distribution of the quantity of interest. Important inference summaries include point es-timation, region estimation and precise hypotheses testing. Those summaries may appropriately be described as the solution to specific decision problems which depend on the particular loss function chosen. The use of a continu-ous loss function leads to an integrated set of solutions where the same prior distribution may be used throughout. Objective Bayesian methods are those which use a prior distribution which only depends on the assumed model and the quantity of interest. As a consequence, objective Bayesian methods pro-duce results which only depend on the assumed model and the data obtained. The combined use of intrinsic discrepancy, an invariant information-based loss function, and appropriately defined reference priors, provides an integrated objective Bayesian solution to both estimation and hypothesis testing prob-lems. The ideas are illustrated with a large collection of non-trivial examples