Chapter

Multiple testing of causal hypotheses

Samantha Kleinberg and Bud Mishra

in Causality in the Sciences

Published in print March 2011 | ISBN: 9780199574131
Published online September 2011 | e-ISBN: 9780191728921 | DOI: http://dx.doi.org/10.1093/acprof:oso/9780199574131.003.0031
Multiple testing of causal hypotheses

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A primary problem in causal inference is the following: From a set of time course data, such as that generated by gene expression microarrays, is it possible to infer all significant causal relationships between the elements described by this data? In prior work (Kleinberg and Mishra, 2009), a framework has been proposed that combines notions of causality in philosophy, with algorithmic approaches built on model checking and statistical techniques for significance testing. The causal relationships can then be described in terms of temporal logic formulæ, thus reframing the problem in terms of model checking. The logic used, PCTL, allows description of both the time between cause and effect and the probability of this relationship being observed. Borrowing from philosophy, prima facie causes are define in terms of probability raising, and then determine whether a causal relationship is significant by computing the average difference a prima facie cause makes to the occurrence of its effect, given each of the other prima facie causes of that effect. However, this method faces many interesting issues confronted in statistical theories of hypothesis testing, namely, given these causal formulæ with their associated probabilities and our average computed differences, instead of choosing an arbitrary threshold, how do we decide which are ‘significant’? To address this problem rigorously, the chapter uses the concepts of multiple hypothesis testing (treating each causal relationship as a hypothesis), and false discovery control. In particular, the chapter applies the empirical Bayesian formulation proposed by Efron (2004). This method uses an empirical rather than theoretical null, which has been shown to be better equipped for cases where the test statistics are dependent ‐ as may be true in the case of complex causal structures. The general approach may be used with many of the traditional philosophical theories where thresholds for significance must be identified.

Keywords: causal significance; multiple testing; false discovery rate; temporal logic

Chapter.  8723 words.  Illustrated.

Subjects: Logic

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