رهيافت بيزي نيمه پارامتري و كاربرد آن در مدل هاي با اثرات آميخته

The Semi-Parametric Bayesian Approach and its Application in Mixed Effects Models

Generalized Linear Models with Mixed Effects are most usual models are used to analyze dependent data in various sciences such as Medical research, Biologic studies, Economics and etc. Since application of appropriate estimation methods for es¬timating parameters in these models is very important for achieving results and due to frequent application of the Bayesian Statistics in fitting complicated models, in this ar¬ticle the above mentioned subject is studied using Bayesian Semi-parametric methods. An important issue in using these methods is the application of an appropriate process for generating Mixed Effects Distributions. This thesis taking in to consideration the distribution of Mixed Effects follow a Dirichlet process with a specific Base Measure and known Precision Parameter, surveys a Bayesian Hierachical Semi-parametric models for analyzing dependent data in General Linear Regression. So, first we are going to introduce Dirichlet Process and the method of its simulation using various models, then, weʹll use it as a process for generating prior distributions in different kinds of models. Next, weʹll find Full Conditional Posterior Distributions of parameters in Linear Regression Models whit Mixed Effects and using Bayesian Approach weʹll do Statistical Inferences by Gibbs Sampling Algotithm. Finally, different models will be fitted to real data of various sci¬ences in order to demonstrate the advantage of applying the Bayesian Semi-parametric methods in comparison over with common methods.