Identifying the Causal Structure from the Correlation Matrix

The structure with the best posterior probability as calculated by the Cooper and Herskovits formula does not necessarily give the correct causal structure. There is a need to understand why the posterior probability structure sometimes gives incorrect structures. A new norm is identified that simplifies identification of the causal structure. In this research some theorems are proved to identify the causal structure. The aim of the research on which this article reports, was to place the first two theorems that this author proved about the norm, that gives an alternative to the Cooper and Herskovits algorithm, in the public domain. There are a number of theorems still not proven and other researchers can give valuable input if they follow the same approach. For a tree structure the best posterior probability structure gives the correct causal structure, however when v-structures are present there is often a discrepancy between the actual causal structure and the highest posterior probability structure. This article helps to clarify this situation and recommends an approach that should eventually lead to a better understanding of causal processes.