", first encountered by Pearson in 1899 , refers to the phenomenon whereby an event C increases the probability of E in a given population p and, at the same time, decreases the probability of E in every subpopulation of p."

“Mr. Holmes receives a telephone call from his neighbor Dr. Watson who states that he hears the sound of a burglar alarm from the direction of of Mr. Holmes' house. While preparing to rush home, Mr. Holmes recalls that Dr. Watson is known to be a tasteless practical joker...”

“Haavelmo was the first to recognize the capacity of economic models to guide policies. This paper describes some of the barriers that Haavelmo’s ideas have had to overcome, and lays out a logical framework that has evolved from Haavelmo’s insight and matured into a coherent and comprehensive account of the relationships between theory, data and policy questions. The mathematical tools that emerge from this framework now enable investigators to answer complex policy and counterfactual questions using simple routines, some by mere inspection of the model’s structure.”

“Traditional statistics is strong in devising ways of describing data and inferring distributional parameters from sample. Causal inference requires two additional ingredients: a science-friendly language for articulating causal knowledge, and a mathematical machinery for processing that knowledge, combining it with data and drawing new causal conclusions about a phenomenon.”

“A quantity Q is identifiable, given a set of assumptions A, iffor any two models M1 and M2 that satisfy A, we have”

“The research questions that motivate most quantitative studies in the health, social and behavioral sciences are not statistical but causal in nature. For example, what is the efficacy of a given drug in a given population? Whether data can prove an employer guilty of hiring discrimination? What fraction of past crimes could have been avoided by a given policy? What was the cause of death of a given individual, in a specific incident? These are causal questions because they require some knowledge of the data-generating process; they cannot be computed from the data alone.”

“When loops are present, the network is no longer singly connected and local propagation schemes will invariably run into trouble.. If we ignore the existence of loops and permit the nodes to continue communicating with each other as if the network were singly connected, messages may circulate indefinitely around the loops and process may not converges to a stable equilibrium... Such oscillations do not normally occur in probabilistic networks... which tend to bring all messages to some stable equilibrium as time goes on. However, this asymptotic equilibrium is not coherent, in the sense that it does not represent the posterior probabilities of all nodes of the network.”