Towards a Statistical Foundation in Combining Structures of Decomposable Graphical Models 1
Sung-Ho Kim · 2000
Summary Graphical models oer simple and intuitive interpretations in terms of conditional independence relationships, and these are especially valuable when large numbers of variables are involved. In some settings restrictions upon experiments, number of variables, and other forms of data collection may result in our being able to estimate only parts of a large graphical model. Consider a collectionC of submodels of a decomposable graphG. In this article, we address the problem of combining component graphical models, and a theory is derived to the eect that one can combine the collection C of decomposable graphs,G1;G2; ;Gm, into a larger decomposable graph, H, of the variables that are involved in G so that the conditional independence relationships inG1;G2; ;Gm may be preserved inH. It is also shown that theH which contains the actual graphG as a subgraph is determined uniquely.