Provides connection between causes and probabilities. Helps enumerate testable implications of a causal model i.e can allow it to be represented in a compact set which allows for queries to be made into that specific set and thus more realistic estimates.

d-separation criterion

Used to infer causal direction by modeling P(y) as a convolution of two non Gaussian distributions, in a linear model X -> Y with non Gaussian noise. P(x) is arguably less Gaussian than P(y), and this 'less' can be measured numerically to give evidence of a direction of causality.

Shimizu et al Method

Based on detecting 'shocks' (local environment changes) and tracing their effects to determine causal direction.

Tian and Pearl Method

Multiple methods exist that can be used to determine causal relationships between variables.

University of Michigan - Ann Arbor

The seven tasks the author thinks SCMs accomplish are : 
1. Encoding Causal Assumptions : Allow Transparency and Testability
2. Allows control for confounding and Do-calculus
3. Helps generate algorithms for counterfactuals
4. Mediation analysis and assessment of effects
5. Adaptability, sample selection, validity
6. Allows for missing data
7. Allows causal discovery

7 tasks accomplished by SCM

Pearl, Judea. “The Seven Tools of Causal Inference, with Reflections on Machine Learning.” Communications of the ACM, vol. 62, no. 3, 2019, pp. 54–60., doi:10.1145/3241036.

https://dl.acm.org/doi/pdf/10.1145/3241036

The Seven Tools of Causal Inference, with Reﬂections on Machine Learning

Discerning if assumptions made are plausible, and the necessity of additional assumptions.

Transparency

Allows assumptions to be tested against existing data to gauge their validity.

Testability

As we have seen in discussions, having a graphical representation allows us to find counterfactuals and if possible find ways to control for them.
If the backdoor criterion cannot be applied, we can also use Do calculus.

Control for Confounding and Do-Calculus

Structural equations provide truth values for counterfactuals. Counterfactual reasoning has been formalized for graphical representation. Thus, we can devise algorithms to determine individual outcomes based on a set of characteristics.

Algorithmizing Counterfactuals

Allows identification of mediators. Helps estimate effects - direct or indirect - of variables on one another using counterfactuals and the graphical representation.

Mediation Analysis and Assessment of Effects

Makes model more adaptable. Do-calculus allows for overcoming environmental bias i.e. bridges gaps between study sample and population, by allowing readjustment of learned parameters.

Adaptability, External Validity, Sample Selection

Causal models of 'missingness' allow for determining causal relationships between variables from the semi complete data. When data is complete, these models can generate realistic estimations.

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