Bayesian Statistics Analysis For Semi-Parametric Log-Generalized-Power-Weibull Regression Models

Lifetime data is an important data which is widely presented in various fields. In the lifetime analysis it is easy to find its relationship with many factors, including animal lifetime affected by Cholesterol content level or Blood pressure and others. Here, it is of interest to consider the relationship between lifetime(dependent variable) and the factors (covariates). In order to study what factors have affect the survival time, considerable research has been done for developing lifetime data analysis, classical linear or nonlinear regression are popular measure. In the presence of more complex data, the merely linear or nonlinear can not illustrate all the information of dependent variable. The semi-parametric models not only contain the advantages of parametric model but the advantages of non-parametric model, can be used to describe more practical problems. There are many distributions of life data, but most of them can only suit to data with monotonous hazard function. For the purpose of data with non-monotonous hazard function and data with bathtub-shaped hazard function, log-generalized-power weibull models is studied, and prove that its hazard function can deal with non-monotonic or bathtub-shaped life data.Therefore, the present paper focus on the statistics analysis for semi-parametric log-generalized-power-weibull regression models. Since most of the survival distribution models are very complicated, considerably proportion of survival data analyze are relied on standard methods frequentist inferences. Much extensive literature on Bayesian methods for survival models, very little has been developed for semi-parametric regression models including survival models and others. We propose a new life distribution log-generalized-power-weibull and discuss a complete Bayesian analysis for regression models. We discuss the general Bayesian approach to analyzing weibull models, then deeply analysis the nature of mathematical statistics.First, this article develops a log-generalized-power-weibull regression model based on the semi-parametric, maximum penalized likelihood estimators for both linear coefficients and nonparametric function are obtained on P-splines. Both parametric and nonparametric are obtained by Gauss-Newton. Then prior information of the parametric models are elicited considering the information with prior knowledge. According Bayesian theorem, a posterior distribution is yield. For Bayesian inference, it can be given the conditional marginal distributions that we need to use the Metropolis-Hastings algorithm to generate sample from the respective conditional posteriori densities, by MCMC method a Markov Chain is obtained. Finally, we introduce Bayesian case influence diagnostics based on the Kullback-Leibuler divergence, a Kullback-Leibuler distance, approximate Kullback-Leibuler distance and residual analysis are given, while generalized Cook distance, likelihood distance, WK statistics are analysised. We examine the performance of the influence diagnostics using simulated data.