Graphical Log-linear Models: Fundamental Concepts and Applications

摘要

We present a comprehensive study of graphical log-linear models forcontingency tables. High dimensional contingency tables arise in many areassuch as computational biology, collection of survey and census data and others.Analysis of contingency tables involving several factors or categoricalvariables is very hard. To determine interactions among various factors,graphical and decomposable log-linear models are preferred. First, we exploreconnections between the conditional independence in probability and graphs;thereafter we provide a few illustrations to describe how graphical log-linearmodel are useful to interpret the conditional independences between factors. Wealso discuss the problem of estimation and model selection in decomposablemodels.