Implementation of Belief Propagation Iterative Method on Markov Chains by Designing Bayesian Networks

This paper mainly deals with the analysis of belief propagation iterative method on Bayesian network in terms of Gaussian random variable. This paper designs a duality between graph structures and probability models in terms of belief propagation. A graphical model is designed to represent the probabilistic relationships between random variables. The variables are represented by nodes and the conditional independencies or dependencies are represented by edges. Undirected edges give the correlation between variables which is defined as Markov random field. Directed edges give Casuality relationships between variables defined as Bayesian networks. Graphical models provide a natural tool for dealing with two problems such as uncertainty and complexity that occur throughout applied mathematics and engineering. Many of the classical, multivariate probabilistic systems studied in the fields of statistics, systems engineering, information theory, pattern recognition and statistical mechanics are special cases of the general graphical model formalism. An algorithm is designed for Gaussian belief propagation and the solution for the system of linear equations is obtained. Based on the network this algorithm runs and the convergence is obtained in comparison with other methods.