ABSTRACT
This chapter assumes that a graph is given and need to find its associated edge probabilities, mirroring the Bayesian inference methods and conjugacy analyses. Even when data is missing at random, if observations are missing non ancestrally so that potential explanatory variables remain unobserved in most or all units then even with huge datasets estimation can inevitably turn out to be ambiguous. The chapter demonstrates that there are exact analogues of Bayesian network (BN) propagation algorithms as these apply to saturated probability trees. Propagation of new information using a BN model requires us to perform a pre-processing step. When the probability mass function of the containing population is uncertain the propagation schemes of the posterior edge mean probabilities on the unit by conjugacy are independent of each other. The chapter addresses some practical issues a user might face when modeling a process using a Chain Event Graph (CEG) and using data sources to inform this.
