Causal inference via graphical Markov models

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The research supported by this NSERC Discovery grant focuses on model selection.  Model search is an important part of statistical analyses, particularly in the absence of background knowledge. The main objective of this research is to develop an efficient model search procedure for processes for which some variables may be unobserved. Graphical Markov models have been used to represent processes from diverse fields such as economics, social sciences, computer science, and engineering. In these settings it is often assumed that the process can be represented by a directed acyclic graph (DAG) in which the relevant variables form the vertices of the graph and the presence or absence of arrows between vertices encode the relationships between the variables.  In many applications, the structure of the graph is assumed known.   More recently, graphical models have been used to infer biological interactions from gene expression data. In such settings, where the underlying structure of the graph is unkown, there may be many causal explanations (graphs) that are equivalent in that they are equally consistent with observed data. Recent advances have been made to represent the common aspects of these explanations into one representation, called an equivalence class.   If data is available for only some of the relevant variables, then it is of interest to determine how every causal explanation among the observed variables change in the presence of latent (unobserved) variables.  The work supported by this grant aims to develop a procedure that searches across equivalence classes of DAG models with latent and selection variables.