ABSTRACT

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 covariates.