commonplace book redux

Remark: The exclusion of unmeasured variables from the definition of statistical parameters is devised to prevent one from hiding causal assumptions under the guise of latent variables. Such constructions, if permitted, would qualify any quantity as statistical and would thus obscure the important distinction between quantities that can be estimated from statistical data alone, and those that require additional assumptions beyond the data.

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The sharp distinction between statistical and causal concepts can be translated into a useful principle: behind every causal claim there must lie some causal assumption that is not discernable from the joint distribution and, hence, not testable in observational studies. Such assumptions are usually provided by humans, resting on expert judgment. Thus, the way humans organize and communicate experiential knowledge becomes an integral part of the study, for it determines the veracity of the judgments experts are requested to articulate.

Another ramification of this causal–statistical distinction is that any mathematical approach to causal analysis must acquire new notation. The vocabulary of probability calculus, with its powerful operators of expectation, conditionalization, and marginalization, is defined strictly in terms of distribution functions and is therefore insufficient for expressing causal assumptions or causal claims. To illustrate, the syntax of probability calculus does not permit us to express the simple fact that “symptoms do not cause diseases,’’ let alone draw mathematical conclusions from such facts. All we can say is that two events are dependent – meaning that if we find one, we can expect to encounter the other, but we cannot distinguish statistical dependence, quantified by the conditional probability P(disease | symptom), from causal dependence, for which we have no expression in standard probability calculus.

The preceding two requirements: (1) to commence causal analysis with untested, judgmental assumptions, and (2) to extend the syntax of probability calculus, constitute the two main obstacles to the acceptance of causal analysis among professionals with traditional training in statistics (Pearl 2003c, also sections 11.1.1 and 11.6.4). This book helps overcome the two barriers through an effective and friendly notational system based on symbiosis of graphical and algebraic approaches.

Judea Pearl, Causality, 2009, Section 1.4, p. 39ff