Abstract

One of the most central problems in scientific research is the search for explanations of some aspect of nature for which empirical data is available. One seeks to identify the causal processes explaining the data, in the form of a model of the aspect of nature under study. Although traditional statistical approaches are excellent for finding statistical dependencies in a body of empirical data, they prove inadequate at finding the causal structure in the data. New graphical algorithmic approaches have been proposed to automatically discover the causal structure in the data. Based on strong connections between graph theoretic properties and statistical aspects of causal influences, fundamental assumptions about the data can be used to infer a graphical structure, which is used to construct models describing the exact causal relations in the data. If the data contain correlated errors, latent variables must be introduced to explain the causal structure in the data. There is usually a large set of equivalent causal models with latent variables, representing competing alternatives, which entail similar statistical dependency relations. ;The central problem in this dissertation is the study of the theoretical limits to reliable causal inference. Given a body of statistical distribution information on a finite set of variables, we seek to characterize the set of all causal models satisfying this distribution. Current approaches only characterize the set of models which satisfy limited properties of this distribution, notably its relations of probabilistic conditional independence. Such models are semi-Markov equivalent. Some of these models might however not satisfy other properties of the distribution, which cannot be expressed as simple conditional independence relations on marginal distributions. We seek to go beyond semi-Markov equivalence. To do so, we first formally characterize the variation in graphical structure within a semi-Markov equivalence class of models. We then determine possible consequences of this variation as either experimentally testable features of models, or as testable features of marginal distributions