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Causality and PsychopathologyFinding the Determinants of Disorders and their Cures$
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Patrick Shrout, Katherine Keyes, and Katherine Ornstein

Print publication date: 2011

Print ISBN-13: 9780199754649

Published to Oxford Scholarship Online: November 2020

DOI: 10.1093/oso/9780199754649.001.0001

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PRINTED FROM OXFORD SCHOLARSHIP ONLINE (oxford.universitypressscholarship.com). (c) Copyright Oxford University Press, 2021. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in OSO for personal use. date: 06 December 2021

The Mathematics of Causal Relations

The Mathematics of Causal Relations

Chapter:
3 (p.47) The Mathematics of Causal Relations
Source:
Causality and Psychopathology
Author(s):

Judea Pearl

Publisher:
Oxford University Press
DOI:10.1093/oso/9780199754649.003.0007

Almost two decades have passed since Paul Holland published his highly cited review paper on the Neyman-Rubin approach to causal inference (Holland, 1986). Our understanding of causal inference has since increased severalfold, due primarily to advances in three areas: 1. Nonparametric structural equations 2. Graphical models Symbiosis between counterfactual and graphical methods 3. These advances are central to the empirical sciences because the research questions that motivate most studies in the health, social, and behavioral sciences are not statistical but causal in nature. For example, what is the efficacy of a given drug in a given population? Can data prove an employer guilty of hiring discrimination? What fraction of past crimes could have been avoided by a given policy? What was the cause of death of a given individual in a specific incident? Remarkably, although much of the conceptual framework and many of the algorithmic tools needed for tackling such problems are now well established, they are hardly known to researchers in the field who could put them into practical use. Why? Solving causal problems mathematically requires certain extensions in the standard mathematical language of statistics, and these extensions are not generally emphasized in the mainstream literature and education. As a result, large segments of the statistical research community find it hard to appreciate and benefit from the many results that causal analysis has produced in the past two decades. This chapter aims at making these advances more accessible to the general research community by, first, contrasting causal analysis with standard statistical analysis and, second, comparing and unifying various approaches to causal analysis. The aim of standard statistical analysis, typified by regression, estimation, and hypothesis-testing techniques, is to assess parameters of a distribution from samples drawn of that distribution. With the help of such parameters, one can infer associations among variables, estimate the likelihood of past and future events, as well as update the likelihood of events in light of new evidence or new measurements.

Keywords:   Algebra, Back-door criterion, Causal effect, Endogenous variable, Independence, Linear equation, Mediation analysis, Noncompliance, Path diagram, Sufficient set

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