Multiple testing of causal hypotheses

Samantha Kleinberg, Bud Mishra

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

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 complexcausal structures. The general approach may be used with many of the traditional philosophical theories where thresholds for significance must be identified.

Original languageEnglish (US)
Title of host publicationCausality in the Sciences
PublisherOxford University Press
ISBN (Electronic)9780191728921
ISBN (Print)9780199574131
DOIs
StatePublished - Sep 22 2011

Keywords

  • Causal significance
  • False discovery rate
  • Multiple testing
  • Temporal logic

ASJC Scopus subject areas

  • Mathematics(all)

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