Table 1.

Selected milestones in the development of modern causal analysis.

Milestone	Key Ideas
Path analysis (Wright, 1921) [65]	Variations in effects around their mean values depend on variations in their direct causes.
Counterfactual causation, potential outcomes (Neyman, 1928 [73]; Rubin, 2005 [57])	Differences in causes make their effects different from what they otherwise would have been.
Interventional causation in simultaneous equation models (Haavelmo, 1943 [23])	Exogenously fixing some variables at specified values changes probability distributions of variables that depend on them. Conditioning differs from fixing values [44].
Causal ordering of variables in simultaneous structural equation models (SEMs) (Simon, 1953, 1954 [54,55])	Causes are exogenous to their direct effects. Changes in causes create changes in their direct effects to restore equilibrium.
Predictive causation (Granger causation) in linear time series Wiener, 1956 [74], Granger, 1969 [71]	Past and present changes in causes help to explain and predict future changes in their effects. The future of an effect is not conditionally independent of the past of its causes, given its own past.
Causal loop diagrams (Maruyama, 1963 75])	Dynamic systems adjust until they reach equilibrium. The equilibrium is caused and explained by a balance of the mechanisms that act to change it [38].
Quasi-experiments. Internal and external validity of causal conclusions (Campbell and Stanley, 1963 [76])	Differences in effects are explained by differences in causes and are not fully explained by differences in other factors.
Causal discovery algorithms (Glymour and Scheines, 1986; Glymour et al., 2019 [19, 20])	Conditional independence and dependence relationships in data constrain the set of possible causal models for the data-generating process.
Interventional causation and causal ordering (Simon and Iwasaki, 1988 [56])	Exogenously changing causes changes the probability distributions of their direct effects.
Causal Bayesian networks, structural causal models, nonparametric SEMs, and conditional independence and dependence (Pearl, 2000 [41])	Effects are not conditionally independent of their direct causes, given the values of other variables. Conditioning on common effects induces dependence between parents that are conditionally independent.
Transfer entropy [72] and directed information	Information flows from direct causes to their effects over time. Transfer entropy generalizes Granger causation.
Functional causal models (Shimuzu et al., 2006 [58])	An effect is often a simple (e.g., additive) function of its direct causes and random noise.
Transportability (Lee and Honovar, 2013; Bareinboim and Pearl, 2013 [30, 5])	Invariance of causal mechanisms (represented by CPTs) enables generalization of causal findings across studies.
Invariant causal prediction (ICP) (Peters et al., 2016; Prosperi et al., 2020 [45, 47])	Causal laws are universal: if levels for all of the direct causes of an effect are the same, then the conditional probability distribution of the effect should be the same across settings (e.g., studies) and interventions.