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August 2012 Counterfactual analyses with graphical models based on local independence
Kjetil Røysland
Ann. Statist. 40(4): 2162-2194 (August 2012). DOI: 10.1214/12-AOS1031

Abstract

We show that one can perform causal inference in a natural way for continuous-time scenarios using tools from stochastic analysis. This provides new alternatives to the positivity condition for inverse probability weighting. The probability distribution that would govern the frequency of observations in the counterfactual scenario can be characterized in terms of a so-called martingale problem. The counterfactual and factual probability distributions may be related through a likelihood ratio given by a stochastic differential equation. We can perform inference for counterfactual scenarios based on the original observations, re-weighted according to this likelihood ratio. This is possible if the solution of the stochastic differential equation is uniformly integrable, a property that can be determined by comparing the corresponding factual and counterfactual short-term predictions.

Local independence graphs are directed, possibly cyclic, graphs that represent short-term prediction among sufficiently autonomous stochastic processes. We show through an example that these graphs can be used to identify and provide consistent estimators for counterfactual parameters in continuous time. This is analogous to how Judea Pearl uses graphical information to identify causal effects in finite state Bayesian networks.

Citation

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Kjetil Røysland. "Counterfactual analyses with graphical models based on local independence." Ann. Statist. 40 (4) 2162 - 2194, August 2012. https://doi.org/10.1214/12-AOS1031

Information

Published: August 2012
First available in Project Euclid: 23 January 2013

zbMATH: 1257.62112
MathSciNet: MR3059080
Digital Object Identifier: 10.1214/12-AOS1031

Subjects:
Primary: 60G44 , 60G55 , 62N04 , 92D30

Keywords: Causal inference , change of probability measures , event history analysis , local independence , marked point processes , Stochastic analysis

Rights: Copyright © 2012 Institute of Mathematical Statistics

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Vol.40 • No. 4 • August 2012
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