|" Bayesian Isotonic Estimation for Exponential Family and Beyond"
| Jayanta Kumar Pal , Ph.D.
SAMSI and Duke University
Mon., October 22, 2007
In the restricted parameter estimation, the use of exponential family have been introduced to
include applications from several scientific studies. The MLE based approach or the smoothing
type estimators have been studied using monotone link functions. In this paper, we introduce
Bayesian techniques to investigate such methods in a general scenario, with illustrations to
special examples such as binomial, Poisson etc. The conjugate priors in the exponential family
problem helps us to obtain posterior distributions with similar expressions. The log-concavity
of the posterior densities allow us to use adaptive rejection sampling for the individual draws.
An MCMC method involving Gibbs sampler is developed to sample from that posterior which
yields credible regions for the parameters. We modify our method to include change-point
estimation as well, where the underlying parameter curve has some known or unknown change-
point. Finally, the method is extended to semiparametric models, where the link function
consists of a monotone function of one particular covariate and a linear model on the other