Research and application of causal inference I have been reading Pearl's book to understand how Bayesian networks and causal discovery might work. Other than Pearl, I haven't yet found a rigorous, systematic approach to causal inference from observational data. The theorems and algorithms he presents (e.g. Inductive Causation) look convincing to me, however, it appears that causal discovery is very much in research. I was wondering if anyone had any experience applying any of this research or knows of any other, strongly supported methods of causal inference.
 A: Causal inference, in the form of many algorithms that evolved from ideas Pearl (et. al.) presented in the papers the book you mention is based on are abundant,  sometimes with marked success. This book will give plenty of algorithms and applications. 
One striking application is the construction of a Bayesian network for the diagnosis of complicated lung conditions. The network performs almost as well as a team of expert lung doctors. There are many others for, e.g., robots traveling through a maze, computer vision, OCRs etc.   
A: There are many tools for finding causal links between measured variables from observational data alone other than Bayesian networks. An early one is Granger causality. 
The approach of Granger has been generalized to information theoretic tools such as Transfer Entropy and Causation Entropy. In these methods one identifies flows of information between variables. 
There are many differences between Pearl's approach and the methods mentioned here. The Scholarpedia page on Granger Causality contains some excerpts from Clive Granger's works in which he elaborates on the distinction between this type of causality and intervention based causality.
I've only read a little of Pearl, but being familiar with the information flow approaches, I will try to comment on some differences I was picking up on from what I read. The most general might be that these information flow based methods are only saying that $X$ has a causal influence on $Y$ given the set of variables that have been measured (as opposed to looking for a more universal causation that exists in the space of all potential variables).
This relaxation of the use of the word "cause" seems to lead to a bit more flexibility. Firstly, the measured data can be obtained from passive observation alone (useful when the data was measured before you were called in to analyze it, or when intervening in the system in any way would fundamentally change the system). Further the outcome is more general -- a directed graph, as opposed to an acyclic directed graph. 
Note: This is not to say one is better than the other. Pearl and information causality do slightly different things and the user needs to decide which notion of causality is appropriate for their setting.
