Decomposable Hierarchical Model

This paper aims at some properties of decomposable hierarchical model. First I discussed the decomposable generating class and get that C is decomposable if and only if C =k (G ( C )) and G ( C )is decomposable. Then I gave a recursion decomposition of C by the hyperedge decomposition of a decomposable generating hypergraph .By this recursion decomposition C can decompose into all of the subgenerating class induced by a element of C . At last I gave the most simple result of estimation and test for a decomposable hierarchical model. I also discussed the junction property, the induced-subtree property, the running intersection property of a generating class tree and the relationship among them.