Causal model

In philosophy of science, a causal model (or structural causal model) is a conceptual model that describes the causal mechanisms of a system. Causal models can improve study designs by providing clear rules for deciding which independent variables need to be included/controlled for. Causal models are mathematical models representing causal relationships within an individual system or population. They facilitate inferences about causal relationships from statistical data. They can teach us a good deal about the epistemology of causation, and about the relationship between causation and probability. They have also been applied to topics of interest to philosophers, such as the logic of counterfactuals, decision theory, and the analysis of actual causation. In philosophy of science, a causal model (or structural causal model) is a conceptual model that describes the causal mechanisms of a system. Causal models can improve study designs by providing clear rules for deciding which independent variables need to be included/controlled for. They can allow some questions to be answered from existing observational data without the need for an interventional study such as a randomized controlled trial. Some interventional studies are inappropriate for ethical or practical reasons, meaning that without a causal model, some hypotheses cannot be tested. Causal models can help with the question of external validity (whether results from one study apply to unstudied populations). Causal models can allow data from multiple studies to be merged (in certain circumstances) to answer questions that cannot be answered by any individual data set. Causal models are falsifiable, in that if they do not match data, they must be rejected as invalid. Causal models have found applications in signal processing, epidemiology and machine learning. Pearl defines a causal model as an ordered triple ⟨ U , V , E ⟩ {displaystyle langle U,V,E angle } , where U is a set of exogenous variables whose values are determined by factors outside the model; V is a set of endogenous variables whose values are determined by factors within the model; and E is a set of structural equations that express the value of each endogenous variable as a function of the values of the other variables in U and V. Aristotle defined a taxonomy of causality, including material, formal, efficient and final causes. Hume rejected Aristotle's taxonomy in favor of counterfactuals. At one point, he denied that objects have 'powers' that make one a cause and another an effect.:264 Later he adopted 'if the first object had not been, the second had never existed' ('but-for' causation).:265 In the late 19th century, the discipline of statistics began to form. After a years-long effort to identify causal rules for domains such as biological inheritance, Galton introduced the concept of mean regression (epitomized by the sophomore slump in sports) which later led him to the non-causal concept of correlation. As a positivist, Pearson expunged the notion of causality from much of science as an unprovable special case of association and introduced the correlation coefficient as the metric of association. He wrote, 'Force as a cause of motion is exactly the same as a tree god as a cause of growth' and that causation was only a 'fetish among the inscrutable arcana of modern science'. Pearson founded Biometrika and the Biometrics Lab at University College London, which became the world leader in statistics.