For most researchers in the ever growing fields of probabilistic graphical models, belief networks, causal influence and probabilistic inference, ACM Turing award winner Dr. Judea Pearl and his seminary papers on causality are well-known and acknowledged. Representation and determination of Causality, the relationship between an event (the cause) and a second event (the effect), where the second event is understood as a consequence of the first, is a challenging problem. Over the years, Dr. pearl has written significantly on both Art and Science of Cause and Effect. In this book on “Causality: Models, Reasoning and Inference”, the inventor of Bayesian belief networks discusses and elaborates on his earlier workings including but not limited to Reasoning with Cause and Effect, Causal inference in statistics, Simpson's paradox, Causal Diagrams for Empirical Research, Robustness of Causal Claims, Causes and explanations, and Probabilities of causation Bounds and identification.
In these eleven chapters followed by an epilogue, Dr. Pearl’s manuscript postulates representational and computational foundation for the processing of information under uncertainty. It commences with introduction of simpler concepts in Bayesian inference, causality and corresponding proves. However, as text progresses into causal vs. statistical concepts along with theory of inferred causation, the theorems get arduous, somewhat counter-intuitive and the text becomes demanding to keep up. Chapter 3 is an interesting read where causality is discussed in context of philosophy and history. As Dr. Liu states, Judea Pearl’s thesis regarding statistics that it deals with quantitative constructs like mean, variance, correlation, regression, dependence, conditional independence, association, likelihood, collapsibility, risk ratio, odd ratio, marginalization, conditionalization, etc. Meanwhile the causal analysis deals with the topics of randomization, influence, effect, confounding, disturbance, correlation, intervention, explanation and attribution. One of the challenges while following Dr. Pearl’s work is that it abstracts causation discussing it in mathematical and philosophical manner without providing concrete mathematical and computational model for applied research. I believe the book provides great foundation for formal representation of causal analysis and its components, such as do(x) to represent intervention.
Automated Reasoning Group at UCLA has made some strides in this area however the applied research aspects of this formalism still needs to be ‘tightly bound’ by reason of scarcity of empirical evidence for the algorithms in practice.