Causal graphs and conditional independence

Causal relationships are often illustrated by directed graphs with arrows pointing 
from causes to effects. These graphs need not be acyclic, reflecting the occurrence
of feedback loops in nature. The causal graph becomes a causal model when the arrows
are assigned interventional probabilities, i.e., the probability distribution on the
effect when the cause is set to a given value. The classical result of Judea Pearl (1985)
establishes how this causal graph encodes the conditional independence relationships 
between subsets of nodes when the nodes are random variables and the graph is acyclic.
This has been further extended to more sophisticated situations, e.g., when the nodes
are stochastic processes and the conditional independence statements involve 
differentiation between the processes' past and future. In my talk, 
I will present a unifying view of these results, which allows for slight extensions 
or at least alternative proofs of some of them.