Causal inference

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Causal inference is the process of drawing a conclusion about a causal connection based on the conditions of the occurrence of an effect. The main difference between causal inference and inference of association is that the former analyzes the response of the effect variable when the cause is changed.[1][2] The science of why things occur is called etiology.


Inferring the cause of something has been described as

  • "...reason[ing] to the conclusion that something is, or is likely to be, the cause of something else".[3]
  • "Identification of the cause or causes of a phenomenon, by establishing covariation of cause and effect, a time-order relationship with the cause preceding the effect, and the elimination of plausible alternative causes."[4]


Epidemiological studies employ different epidemiological methods of collecting and measuring evidence of risk factors and effect and different ways of measuring association between the two. A hypothesis is formulated, and then tested with statistical methods (see Statistical hypothesis testing). It is statistical inference that helps decide if data are due to chance, also called random variation, or indeed correlated and if so how strongly.

Common frameworks for causal inference are structural equation modeling and the Rubin causal model.[citation needed]

In epidemiology[edit]

Epidemiology studies patterns of health and disease in defined populations of living beings in order to infer causes and effects. An association between an exposure to a putative risk factor and a disease may be suggestive of, but is not equivalent to causality or correlation does not imply causation. Historically, Koch's postulates have been used since the 19th century to decide if a microorganism was the cause of a disease. In the 20th century the Bradford Hill criteria, described in 1965[5] have been used to assess causality of variables outside microbiology, although even these criteria are not exclusive ways to determine causality.

In molecular epidemiology the phenomena studied are on a molecular biology level, including genetics, where biomarkers are evidence of cause or effects.

A recent trend[when?] is to identify evidence for influence of the exposure on molecular pathology within diseased tissue or cells, in the emerging interdisciplinary field of molecular pathological epidemiology (MPE).[third-party source needed] Linking the exposure to molecular pathologic signatures of the disease can help to assess causality.[third-party source needed] Considering the inherent nature of heterogeneity of a given disease, the unique disease principle, disease phenotyping and subtyping are trends in biomedical and public health sciences, exemplified as personalized medicine and precision medicine.[third-party source needed]

In computer science[edit]

Determination of cause and effect from joint observational data for two time-independent variables, say X and Y, has been tackled using asymmetry between evidence for some model in the directions, X → Y and Y → X. One idea is to incorporate an independent noise term in the model to compare the evidences of the two directions.

Here are some of the noise models for the hypothesis Y → X with the noise E:

  • Additive noise:[6]
  • Linear noise:[7]
  • Post-non-linear:[8]
  • Heteroskedastic noise:
  • Functional noise:[9]

The common assumption in these models are:

  • There are no other causes of Y.
  • X and E have no common causes.
  • Distribution of cause is independent from causal mechanisms.

On an intuitive level, the idea is that the factorization of the joint distribution P(Cause,Effect) into P(Cause)*P(Effect | Cause) typically yields models of lower total complexity than the factorization into P(Effect)*P(Cause | Effect). Although the notion of “complexity” is intuitively appealing, it is not obvious how it should be precisely defined.[9]


Graduate courses on causal inference have been introduced to the curriculum of many schools.

See also[edit]


  1. ^ Pearl, Judea (1 January 2009). "Causal inference in statistics: An overview" (PDF). Statistics Surveys. 3: 96–146. doi:10.1214/09-SS057. 
  2. ^ Morgan, Stephen; Winship, Chris (2007). Counterfactuals and Causal inference. Cambridge University Press. ISBN 978-0-521-67193-4. 
  3. ^ "causal inference". Encyclopædia Britannica, Inc. Retrieved 24 August 2014. 
  4. ^ John Shaughnessy; Eugene Zechmeister; Jeanne Zechmeister (2000). Research Methods in Psychology. McGraw-Hill Humanities/Social Sciences/Languages. pp. Chapter 1 : Introduction. ISBN 0077825365. Retrieved 24 August 2014. 
  5. ^ Hill, Austin Bradford (1965). "The Environment and Disease: Association or Causation?". Proceedings of the Royal Society of Medicine. 58 (5): 295–300. PMC 1898525free to read. PMID 14283879. 
  6. ^ Hoyer, Patrik O., et al. "Nonlinear causal discovery with additive noise models." NIPS. Vol. 21. 2008.
  7. ^ Shimizu, Shohei, et al. "DirectLiNGAM: A direct method for learning a linear non-Gaussian structural equation model." The Journal of Machine Learning Research 12 (2011): 1225-1248.
  8. ^ Zhang, Kun, and Aapo Hyvärinen. "On the identifiability of the post-nonlinear causal model." Proceedings of the Twenty-Fifth Conference on Uncertainty in Artificial Intelligence. AUAI Press, 2009.
  9. ^ a b Mooij, Joris M., et al. "Probabilistic latent variable models for distinguishing between cause and effect." NIPS. 2010.
  10. ^
  11. ^

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