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Causal inference

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Title: Causal inference  
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Subject: Causal inference, Inductive reasoning, Multivariate statistics, Statistical inference, Regression analysis
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Causal inference

Causal inference is the process of drawing a conclusion about a [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 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.

In epidemiology

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 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). Linking the exposure to molecular pathologic signatures of the disease can help to assess causality. 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.

In computer science

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] Y = F(X)+E
  • Linear noise:[7] Y = pX + qE
  • Post-non-linear:[8] Y = G(F(X)+E)
  • Heteroskedastic noise: Y = F(X)+E.G(X)
  • Functional noise:[9] Y = F(X,E)

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]

See also


  1. ^ Pearl, Judea (1 January 2009). "Causal inference in statistics: An overview". Statistics Surveys 3: 96–146.  
  2. ^ Morgan, Stephen; Winship, Chris (2007). Counterfactuals and Causal inference. Cambridge University Press.  
  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.  
  5. ^ Hill, Austin Bradford (1965). "The Environment and Disease: Association or Causation?".  
  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.

External links

  • NIPS 2013 Workshop on Causality
  • Causal inference at the Max-Planck-Institute for Intelligent Systems Tübingen
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