Unifying Causal Models with Trek Rules
In many scientific contexts, different investigators experiment with or observe different variables with data from a domain in which the distinct variable sets might well be related. This sort of fragmentation sometimes occurs in molecular biology, whether in studies of RNA expression or studies of protein interaction, and it is common in the social sciences. Models are built on the diverse data sets, but combining them can provide a more unified account of the causal processes in the domain. On the other hand, this problem is made challenging by the fact that a variable in one data set may influence variables in another although neither data set contains all of the variables involved. Several authors have proposed using conditional independence properties of fragmentary (marginal) data collections to form unified causal explanations when it is assumed that the data have a common causal explanation but cannot be merged to form a unified dataset. These methods typically return a large number of alternative causal models. The first part of the thesis shows that marginal datasets contain extra information that can be used to reduce the number of possible models, in some cases yielding a unique model.