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.

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.