Probability Bracket Notation, Multivariable Systems and Static Bayesian Networks

Probability Bracket Notation (PBN) is applied to systems of multiple random variables for preliminary study of static Bayesian Networks (BN) and Probabilistic Graphic Models (PGM). The famous Student BN Example is explored to show the local independences and reasoning power of a BN. Software package Elvira is used to graphically display the student BN. Our investigation shows that PBN provides a consistent and convenient alternative to manipulate many expressions related to joint, marginal and conditional probability distributions in static BN.