Searching Across Markov Equivalence Classes of Maximal Ancestral Graphs

• Activity Number: 187
• Type: Contributed
• Date/Time: Tuesday, August 10, 2004 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Computing
• Author(s): Rebecca A. Ali*+ and Thomas Richardson
• Companies: National University of Singapore and University of Washington
• Keywords: maximal ancestral graphs ; joined graphs ; Markov equivalence ; DAG models ; latent variables

Abstract

Graphical Markov models have emerged as a powerful tool for representing diverse data-generating processes. Ancestral graphs enable one to encode the conditional independence relations that arise in directed acyclic graph (DAG) models with latent variables, without explicitly including latent variables in the model (graph). However, for any ancestral graph, there may be several other graphs to which it is Markov equivalent thus making an exhaustive search across ancestral graphs inefficient. We present a joint operation on ancestral graphs which provides a simple representation for their Markov equivalence classes, thereby facilitating the model search process for some given data. We also provide a proof of the global Markov property for joined ancestral graphs. Model searches across equivalence classes of ancestral graphs can be conducted in statistical packages such as gR (for Gaussian models). The ultimate goal of this work is to obtain a full characterization of the structure of Markov equivalence classes for maximal ancestral graphs, thereby extending analogous results for DAGs given by Verma and Pearl (1991), Chickering (1995), and Andersson et al. (1997).