Improper and proper posteriors with improper priors in a Poisson-gamma hierarchical model

In Bayesian analysis, Markov chain Monte Carlo techniques have become so easy to use that it is possible to erroneously generate observations from a posterior distribution that is improper. In this paper we discussed the Poisson-gamma hierarchical model. A flexible prior distribution is discussed, one which allows the user to choose improper priors. Necessary and sufficient conditions are given for the posterior distribution to be proper and for the posterior moments to exist. An example using data on brain lesions for multiple sclerosis patients is presented to demonstrate the difficulty in diagnosing whether the posterior is proper.     

A numerical investigation of wave interactions in dielectricwaveguides with periodic surface corrugations

The modal properties of planar multilayered waveguides with a rectangular surface corrugation are investigated. A rigorous full Floquet numerical analysis is performed for the fundamental TE mode of the infinite periodic structure. The algorithm is based on a boundary element solution of the integral wave equation in the grating region. A generalized transverse resonance-type matrix equation is sought that matches all continuity, periodicity, and boundary conditions. The resonant solutions of this characteristic equation represent all the surface and leaky waves supported by the structure. The exact dispersion characteristics, as well as the amplitudes of the space harmonics are computed and discussed in connection with radiation losses and coupling mechanisms near resonant Bragg conditions. In particular, a specific double-heterostructure GaAs/AlGaAs waveguide geometry is examined in detail