Sung-Ho Kim

Abstract Graphical models offer 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 on experiments and other forms of data collection may result in our being able to estimate only parts of a large graphical model; for example, when the data in a large contingency table are extremely sparse. In other settings, we might use a model building strategy th

Abstract. Necessary and sufficient conditions for collapsibility of a directed acyclic graph (DAG) model for a contingency table are derived. By applying the conditions, we can easily check collapsibility over any variable in a given model either by using the joint probability distribution or by using the graph of the model structure. It is shown that collapsibility over a set of variables can be checked in a sequential manner. Furthermore, a DAG is compared with its moral graph in the context o

Abstract Graphical models offer 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 on experiments and other forms of data collection may result in our being able to estimate only parts of a large graphical model; for example, when the data in a large contingency table are extremely sparse. In other settings, we might use a model building strategy th

Breiman, Friedman, Olshen, and Stone (1984) use a linear combination of prediction risk and tree size as a criterion in search of optimal trees. In this paper we use a linear combination of the above two components and the variable-observation cost as a criterion (C 1) for the same purpose. This paper explicitly represents the relation among nested, pruned subtrees in terms of C 1. Further, the theories in Breiman et al. (1984) concerning the search of optimal trees are generalized.

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 com

Graphs are used effectively in representing model structures in a variety of research fields such as statistics, artificial intelligence, data mining, biological science, medicine, decision science, educational science, etc. We use different forms of graphs according to the nature of the random variables involved. For instance, arrows are used when the relationship is asymmetric as when it is causal or temporal, and undirected edges are used when the relationship is associative.

The estimates from an EM when it is applied to a large causal model of 10 or more categorical variables are often subject to the initial values for the estimates. This phenomenon becomes more serious as the model structure becomes more serious as the model structure becomes more complicated involving more variables. In this regard Wu(1983) recommends among others that EMs are implemented several times with different sets of initial values to obtain more appropriate estimates. in this paper a new