Bayesian Inference for Double Generalized Linear Regression Models of the Inverse Gaussian Distribution

In recent years, double regression models, in which we jointly model the mean and the dispersion (or variance) directly as a function of the explanatory variables, are widely used in many practical problems. Further, the inverse Gaussian distribution is one of the basic models for describing positively skewed data which arise in a variety of applications. Therefore, in this paper we consider Bayesian estimation for the parameters of double generalized linear regression models of the inverse Gaussian distribution. A computational efficient MCMC method which combines the Gibbs sampler and Metropolis-Hastings algorithm is implemented to simultaneously obtain the Bayesian estimates of unknown parameters, as well as their standard deviation estimates. Finally, several simulation studies are presented to illustrate the proposed methodology.