โ Scribed by Koski, Timo; Noble, John M.
No coin nor oath required. For personal study only.
Causality is a notion with a manipulative component. Wold R.H. Strotz and H.O.A. [117] state: '. . . in common scientific usage, (causality) has the following general meaning: z is the cause of y if, by the hypothesis that it is, or would be, possible, by controlling z indirectly, to control y, at least stochastically'.
Hence, causal inference in this chapter is meant to answer to predictive queries about the effect of a hypothetical or pondered manipulation or intervention. 1 Causal predictive inference requires a machinery to signify intervention, i.e. when one actively changes the value of one or more of the variables. Examples of manipulations are medical treatments and manual interceptions in an automatic controller. These change the states in a data-generating mechanism by upsetting the normal forces working on it. This is the basic principle of a 'controlled experiment'. In order to assess whether or not a particular variable has a causal effect on another, the values of that variable are assigned purely at random, by the controller, without reference to any other factors.
1 There are also counter-factual causal inferences of the form of an explanation If and event A had not occurred, then C would not have occurred, which are not explicitly covered here.
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