Bayesian Statistics Seminar
North Carolina State University
presents
Dr. John Monahan
North Carolina State University
"Elliptically Symmetric Families for Bayesian Analysis of Generalized Linear Models"
ABSTRACT
A common approach in importance sampling is to use the Multivariate Normal as an importance sampler. The main idea behind this approach is the second order approximation of the log of the posterior distribution. However, the multivariate Normal is not appropriate when the posterior has heavier tails, which in practice is often the case. We propose two radial-spherical distributions as importance samplers, the Huber and the Elliptical Multivariate Logistic (EMVL) distributions. The appeal of the Huber and the EMVL as importance samplers is that they can be matched to the posteriors to have the same mode and Hessian. In addition both these distributions have exponential tails. The Huber is more flexible, it is Normal close to the mode but its tails are exponential, these can be matched to the `worst' direction of the posterior. We outline the construction of these distributions and present four importance sampling applications.
This is a joint work with Buffy Hudson-Curtis and Stella Karuri
Tuesday, November, 27, 2007
4:00 - 5:00 pm
208 Patterson Hall