Generalized linear models and beyond: An innovative approach from Bayesian perspective

In this dissertation we develop an innovative approach to analyze the scientific studies using the generalized linear models (GLM) and beyond. We develop the regression estimator, a new algorithm for fitting GLM and different model diagnostic technique for GLM. In the context of the longitudinal study, we present the Bayesian analysis of the generalized multivariate gamma distribution for the generalized multivariate analysis of variance (GMANOVA) model. We demonstrate the method for modeling longitudinal studies as state space dynamic model. We accomplish this by introducing the power filter for dynamic generalized linear models (DGLM). An information processing optimality property of the power filter is presented and we establish the relationship between the Kalman filter and the power filter as well. We develop the Pareto regression model for analyzing the extreme drinking behavior of the alcohol dependence disorder patients.