Abstract Augmenting the graphoid axioms with three additional rules enables us to handle independencies among observed as well as counterfactual variables. The augmented set of axioms facilitates the derivation of testable implications and ignorability conditions whenever modeling assumptions...

Abstract In this issue of the Causal, Casual, and Curious column, I compare several ways of extracting information from post-treatment variables and call attention to some peculiar relationships among them. In particular, I contrast do -calculus conditioning with counterfactual conditioning and...

Abstract This note examines one of the most crucial questions in causal inference: “How generalizable are randomized clinical trials?” The question has received a formal treatment recently, using a non-parametric setting, and has led to a simple and general solution. I will describe this...

Abstract In 1954, Jim Savage introduced the Sure Thing Principle to demonstrate that preferences among actions could constitute an axiomatic basis for a Bayesian foundation of statistical inference. Here, we trace the history of the principle, discuss some of its nuances, and evaluate its...

Abstract Among the many peculiarities that were dubbed “paradoxes” by well meaning statisticians, the one reported by Frederic M. Lord in 1967 has earned a special status. Although it can be viewed, formally, as a version of Simpson’s paradox, its reputation has gone much worse. Unlike...

Abstract This note illustrates, using simple examples, how causal questions of non-trivial character can be represented, analyzed and solved using linear analysis and path diagrams. By producing closed form solutions, linear analysis allows for swift assessment of how various features of the...

Abstract The structural interpretation of counterfactuals as formulated in Balke and Pearl (1994a,b) [ 1 , 2 ] excludes disjunctive conditionals, such as “had $X$ been $x_1~\mbox{or}~x_2$ ,” as well as disjunctive actions such as $do(X=x_1~\mbox{or}~X=x_2)$ . In contrast, the closest-world...

Abstract We consider ways of enabling systems to apply previously learned information to novel situations so as to minimize the need for retraining. We show that theoretical limitations exist on the amount of information that can be transported from previous learning, and that robustness to...

Abstract Non-manipulable factors, such as gender or race have posed conceptual and practical challenges to causal analysts. On the one hand these factors do have consequences, and on the other hand, they do not fit into the experimentalist conception of causation. This paper addresses this...