Bayesci grafik modelleri

Abstract

Posterior distributions obtained by Bayesian approach usually have high dimensions when the models are rather complicated. Therefore, to reach the marjinal distributions from the models is analitically intractable. The aim of the study is to introduce the newest Bayesian practical techniques for the complicated models and to investigate Bayesian graphical model and Gibbs Sampling which is a Markov Chain Monte Carlo method together. BUGS package is used to show how the complicated models are solved iteratively. To understand the conditional structure of the models is very crucial for analysing the complicated models. Graphical models can be used to have a visual information of the structure of these models. Conditional independence allows us to factorize the joint distributions. Samples can be drawn iteratively from the marjinal distributions of the model parameters by Markov Chain Monte Carlo techniques. Then statistical inference can be make easier for the marjinal distiributions. Three different models are investigated in the study. BUGS package is used to have the visual representations of the three models. Gibbs samplings is applied for these models to obtain the marjinal distributions of the model parameters. The result obtained from Gibbs samplings are compared with the classical results in the multiple regression model. The changes in the number of iterations, initial values and the prior distributions of the models parameters are investigated. When the number of the iteration increases, the results are very close to true values. It is also seen in the study that the initial values are not so important if the number of iterations is high.