LARGE CLASSES OF PROPER PRIORS FOR LINEAR-MODELS

We consider the problem of a hierarchical linear model with normal likelihood and variance known in the case where there is very little information about the hyperparameters. We address the problem proposing the use of a very wide class of priors that can be expressed as scale mixtures of normals. Two possibilities are considered: a class based on Double Exponential densities and a class based on Cauchy densities. An example is given to illustrate the techniques.