Causal Reasoning with Ancestral Graphs

Causal reasoning is primarily concerned with what would happen to a system under external interventions. In particular, we are often interested in predicting the probability distribution of some random variables that would result if some other variables were forced to take certain values. One prominent approach to tackling this problem is based on causal Bayesian networks, using directed acyclic graphs as causal diagrams to relate post-intervention probabilities to pre-intervention probabilities that are estimable from observational data. However, such causal diagrams are seldom fully testable given observational data. In consequence, many causal discovery algorithms based on data-mining can only output an equivalence class of causal diagrams (rather than a single one). This paper is concerned with causal reasoning given an equivalence class of causal diagrams, represented by a (partial) ancestral graph. We present two main results. The first result extends Pearl (1995)'s celebrated do-calculus to the context of ancestral graphs. In the second result, we focus on a key component of Pearl's calculus---the property of invariance under interventions, and give stronger graphical conditions for this property than those implied by the first result. The second result also improves the earlier, similar results due to Spirtes et al. (1993)

Two-Loop Diagrams in Causal Perturbation Theory

The scalar two-loop master diagram is revisited in the massive cases needed for the computation of boson and fermion propagators in QED and QCD. By means of the causal method it is possible in a straightforward manner to express the propagators as double integrals. In the case of vacuum polarization both integrations can be carried out in terms of polylogarithms, whereas the last integral in the fermion propagator cannot be expressed by known special functions. The advantage of the method in comparison with Feynman integral calculations is indicated.Comment: 16 pages, latex, the figures can be ordered at the first authors address (A.Aste), the necessary macros are included in the latex-fil

Constructing Influence Diagrams & Causal Loop Diagrams

Causal diagrams, as used in the field of System Dynamics, are important tools for describing the structure of feedback systems. While they cannot be used to infer the dynamics of a system, they provide a powerful way to capture and communicate mental models and other hypotheses about the causes of observed behaviour. The construction of causal diagrams requires an approach that is more disciplined than the usual mind-mapping exercise, while still allowing flexible expression of ideas. The basic ideas described briefly in this guide are intended as an introduction to the art and science of causal-diagram construction. We provide instructions for constructing influence diagrams (IDs) and causal loop diagrams (CLDs)

Causal Diagrams for Structural Engineers

Causal diagrams are logic and graphical tools that depict assumptions about presumed causal relations. Such diagrams have proven effective in tackling a variety of problems in social sciences and epidemiology research yet remain foreign to civil engineers. Unlike the traditional means of examining relationships via multivariable regression, causal diagrams can identify the presence of confounders, colliders, and mediators. Thus, this paper hopes to introduce the big ideas behind causal diagrams (specifically, directed acyclic graphs (DAGs)) and how to create and apply such diagrams to several civil engineering problems. Findings from the presented case studies indicate that civil engineers can successfully use causal diagrams to improve their understanding of complex causation relations, thereby accelerating research and practical efforts

Perturbative Description of the Fermionic Projector: Normalization, Causality and Furry's Theorem

The causal perturbation expansion of the fermionic projector is performed with a contour integral method. Different normalization conditions are analyzed. It is shown that the corresponding light-cone expansions are causal in the sense that they only involve bounded line integrals. For the resulting loop diagrams we prove a generalized Furry theorem.Comment: 34 pages, LaTeX, 2 ancillary files, minor improvements (published version