Directed Acyclic Graphs and Monotonic Effects

Properties of Monotonic Effects on Directed Acyclic Graphs

Various relationships are shown hold between monotonic effects and weak monotonic effects and the monotonicity of certain conditional expectations. Counterexamples are provided to show that the results do not hold under less restrictive conditions. Monotonic effects are furthermore used to relate signed edges on a causal directed acyclic graph to qualitative effect modification. The theory is a...

Generic Directed Acyclic Graphs

Copula directed acyclic graphs

We present a new methodology for selecting a Bayesian network for continuous data outside the widely used class of multivariate normal distributions. The use of bivariate copula densities to model connections between pairs of nodes in the network brings in flexibility in the choice of the distribution. Cand D-vines play a central role in dealing with the high-dimensional aspect of the data, due...

Use of Directed Acyclic Graphs

This supplement describes how counterfactual theory is used to define causal effects and the conditions in which observed data can be used to estimate counterfactual-based causal effects. Basic definitions and language used in causal graph theory are then presented. The graphical separation rules linking the causal assumptions encoded in a diagram to the statistical relations implied by the cau...

Multi-state Directed Acyclic Graphs

This paper continues the line of research on the representation and compilation of propositional knowledge bases with propositional directed acyclic graphs (PDAG), negation normal forms (NNF), and binary decision diagrams (BDD). The idea is to permit variables with more than two states and to explicitly represent them in their most natural way. The resulting representation languages are analyze...