Prior and posterior dirichlet distributions on bayesian networks (BNs)

Bayesian Networks (BNs) is a graphical representation model of some random variables and the relationship between the random variables. It is used to determine the joint probability of some random variables based on the posterior probability of each random variable. The posterior probability is calculated based on the parameters of the prior distribution. Prior distribution used in BNs includes the Dirichlet distribution. It is a conjugate prior for the multinomial distribution. Graph of BNs (belief-network structure) is determined by maximizing the probability of each random variable. One of the algorithms used to maximize it is K2 algorithm. The present research seeks to re-derive the joint probability in the belief-network structure using Dirichlet distribution, and to determine K2 algorithm for the structure. The joint probability obtained is the product of each probability of BNs random variable. The probability shows the dependence of a random variable with the others (parents). Based on these views, K2 algorithm can be used and Probability derived from the structure is considered as the product of the probability of each random variable. The probability of each random variable is calculated with the formula f ( i , π i ) = ∏ j = 1 q i ( N ′ i j + r i − 1 ) ! N i j + N ′ i j + r i − 1 ∏ k = 1 r i ( N i j k + N ′ i j k ) ! N ′ i j k ! . . The belief-network structure is found out by determining a set of parents (πi) probably from random variables. Determination of the parents is based on the maximum probability of any random variable through algorithms K2.