Bayesian inference for the discrete Weibull regression models

The goal of this dissertation was to purpose the Bayesian inference based on five models; the discrete Weibull regression model under type-I right censored data, the zero-inflated and hurdle discrete Weibull regression models, and the zero-inflated and hurdle discrete Weibull regression models under type-I right censored data. Additionally, this study compared the performance of Bayesian estimation under three different prior distributions; uniform noninformative prior, Laplace prior, and normal prior using the random walk Metropolis algorithm as well as the maximum likelihood estimation that studied the performance of parameter estimation via the Monte Carlo simulation technique. In the simulation study, we compared the performance of point estimations in terms of mean square error for the discrete Weibull regression model under type-I right censored data with three dispersions of data; excessive zeros data, under-dispersion data, and over-dispersion data. For the zero-inflated and hurdle discrete Weibull regression models with four cases of a simple explanatory variable. In addition, the zero-inflated and hurdle discrete Weibull regression models under type-I right censored data with a simple explanatory variable. Regarding the confidence interval estimation, we constructed the 95% highest posterior density credible intervals of parameters based on Bayesian estimation to compare the performance in terms of coverage probability and average length with over-dispersion case for the discrete Weibull regression model under type-I right censored data. For the zero-inflated and hurdle discrete Weibull regression models, and the zero-inflated and hurdle discrete Weibull regression models under type-I right censored data with a simple explanatory variable from a uniform distribution. In addition, two real datasets are analyzed to see how the model works in practice.The results of the simulation study for the point estimation showed that, the Bayesian estimation based on Laplace prior is the most appropriate method in terms of mean square error for all five models. In a part of the confidence interval estimation in terms of average length after coverage probability must be taken into account showed that, the Bayesian estimation based on Laplace prior is most appropriate method for the discrete Weibull regression model under type-I right censored data. For the zero-inflated and hurdle discrete Weibull regression models, and the hurdle discrete Weibull regression model under type-I right censored data, the maximum likelihood estimation is most appropriate method for small or moderate sample sizes while the Bayesian estimation based on Laplace prior is most appropriate method for large sample size. For the zero-inflated discrete Weibull regression model under type-I right censored data, the maximum likelihood estimation and Bayesian estimation based on Laplace prior are most appropriate method for small or moderate sample sizes while the Bayesian estimation based on uniform noninformative prior is most appropriate method for large sample size.The Bayesian estimation based on both informative priors for discrete Weibull regression model under type-I right censored data shows the best fitting model, according to the findings of an application to the German health registry data. The Bayesian estimation based on normal prior for the zero-inflated and hurdle discrete Weibull regression models, and Bayesian estimation based on both informative priors for the zero-inflated discrete Weibull regression model under type-I right censored data were also found to be the best fitting models when applied to fish data from the state wildlife biologists.