The Decomposition Of Hierarchical Model And Its Applications

The pg-decomposition of graph also decompositions of generating class and hyper-graph are denned in this paper. Dcompositions of a hypergraph by separators with special property (p-decomposition) are investigated which have additional property that they do not generate new maximal prime subhypergraphs ( mp-subhypergraphs ). Such decom-positions lead to a minimal system of derived subhypergraphs. Just all of the maximal prime subhypergraphs compose the derived system.The likelihood maiximal estimation can be completed on sub-hierarchical models attributing to the p-decomposition of hypergraph. P-decompositions can be specified through a D-ordered sequence of the maximal prime subhypergraphs, In this paper we show that every hypergraph H can successively be decomposed such that a unique minimal system of prime subhypergraphs is derived which is the system of mp-subhypergraphs of H. The p-separator of a hypergraph is the pg-separator of the graph.