Abstract:

Human beings organize their intuitive understanding of the world in terms of causes and effects. Primitive humanity posited gods and spirits as invisible causes of phenomena they did not comprehend. As our attempts to understand the world began to be formalized and codified as empirical science, the emphasis on discerning cause-effect relationships remained. Though we, the modern humanity, are armed with powerful computers, sophisticated technology, and highly developed mathematics and statistics, our fundamental questions remain the same as those of our cave dwelling ancestors - we seek to understand the causes of windfalls and misfortunes that befall us, what effects our actions have, and what would happen if the past were different from what it is. This thesis will address these ancient questions with the rigor and generality of modern mathematics.

Using the framework of graphical causal models which formalizes a variety of causal queries, such as causal effects, counterfactuals and path-specific effects as certain types of probability distributions, I will develop algorithms which will evaluate these probability distributions from available information; prove that whenever these algorithms fail to evaluate a query, no other method could succeed; provide characterizations based on directed graphs for cases where these algorithms do succeed; and finally show how a class of constraints placed on the causal model by its directed graph are due to conditional independence in these probability distributions, and how these conditional independencies can be exploited for testing causal theories.