Counterfactual inferences

In the days of the hegemony of logic as the main working tool for philosophers of science, the intuition that laws of nature supported counterfactual inferences was very difficult to support. Not only do bodies which fall under gravity in the proximity of a spherical object display a pattern which can be described as... 

If we update the basis of chemistry to include the heterogeneous regress of charges. Coulomb forces between ions, electron transfer and so on, once again a repertoire of powerful particulars is available to sustain counterfactual inferences. The intuition that samples of ammonia and hydrochloric acid would yield ammonium chloride if they were collocated is sustained by the continuity in space and time of the ions that electron exchange has created. The equation... 

The real issue behind all these flaws of these approaches is that one has to actually define the causal effect of interest and establish a corresponding iden-tifiability result that expresses this causal quantity of interest as a statistical estimand (i.e., as a mapping applied to the data distribution) under a set of assumptions about the data-generating process. This is precisely what causal inference is all about. Causal inference is concerned with posing causal models that code a set of realistic assumptions about the data-generating process and that allow the definition of intervention-specific counterfactual outcomes. Causal effects can now be defined as a difference between the distributions of two intervention-specific counterfactuals. An identifiability result expresses... 

This chapter provides a broad introduction to the state of the art in general causal inference methods with an eye toward safety analysis. In brief, the estimation roadmap begins with the construction of a formal structural causal model of the data that allows the definition of intervention-specific counterfactual outcomes and causal effects defined as functionals of the distributions of these counterfactuals. The establishment of an identifiability result allows the causal parameter to be recast as an esti-mand within a statistical model for the observed data, thus translating the causal question of interest into an exercise in statistical estimation and inference. This exercise is nontrivial in (typically nonparametric) statistical models that are large enough to contain the true data-generating distribution. 

Usually statistics on occupational accidents are presented on the aggregate level. Risk assessment of individual workers is complicated, since it requires detailed information on outcomes of all workers at risk, not only the accident casualties. Information gathering is usually initiated when occupational accidents occur the counterfactual— workers who under the same circumstances did not get involved in an accident— is not observed. For instance, Rivas et al. (2011) analyze with the help of data-mining techniques 62 questionnaires to be completed whenever an accident occurred. They conclude that data-mining outperform conventional statistics in terms of the predictive function and the possibility of identifying interactions between variables with a bearing on accidents. However, the question is whether inferences drawn from a sample of accidents only can be extrapolated to the workers who did not get involved in... 

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