Bayesian Estimation Of Parameters In A Generalized Logistic Model

Logistic regression model is one of the generalized linear models, which is based on the distribution of the 0- 1 model and mainly used in epidemiological research. Some research is monotone increasing and the process of growth is limit, contrast or explore the risk factors of some diseases, however, the generalized Logistic regression is used in the application of reliability theory and survival analysis model in real life, there are many kinds of model the variables in the form of it. We generalize the Logistic regression model in the case of considering the geometric distribution.Scholars from all over the word have discussed this type of model parameter estimation, but did not use the Bayesian approach to its estimation parameters, Bayesian approach is an important method of statistical research,and it has the advantages which the frequentist statistics do not have. Therefore, the Bayesian approach is applied to the model: Geometric distribution under the Bayesian estimation of the generalized Logistic regression model.Firstly, we consider the single parameter model by maximum likelihood and Bayesian estimation method to estimate the parameters in the model,When using Bayesian methods were selected normal distribution, joint distribution as one by one the prior distribution parameter estimation, and estimation results are compared; Secondly, in the multi-parameter model, we use the Bayesian methods?and select the different prior distributions: no generalized information prior distribution normal prior joint distribution and joint prior distribution. The bayesian estimation is calculated respectively, and compare different prior information on the impact of estimated results. Due to geometric distribution under generalized Logistic regression model is complex,the Bayesian estimation of integral can not solve. Therefore, we through the OpenBUGS data simulation software, and use the Gibbs sampling method to extract posterior samples are numerically simulated, and draw the conclusion.