Causes of Effects via a Bayesian Model Selection Procedure

TL;DR

This paper introduces a Bayesian model selection approach to identify the best data subset satisfying causal inference conditions, improving bounds on the probability of causation in individual cases.

Contribution

It proposes a novel variable and a model selection framework to optimize data subsampling for causal inference, advancing the methodology for assessing causation.

Findings

Effective identification of data subsets satisfying causal assumptions.

Application demonstrates practical utility in educational research.

Improved bounds on probability of causation using Bayesian model selection.

Abstract

In causal inference, and specifically in the \textit{Causes of Effects} problem, one is interested in how to use statistical evidence to understand causation in an individual case, and so how to assess the so-called {\em probability of causation} (PC). The answer relies on the potential responses, which can incorporate information about what would have happened to the outcome as we had observed a different value of the exposure. However, even given the best possible statistical evidence for the association between exposure and outcome, we can typically only provide bounds for the PC. Dawid et al. (2016) highlighted some fundamental conditions, namely, exogeneity, comparability, and sufficiency, required to obtain such bounds, based on experimental data. The aim of the present paper is to provide methods to find, in specific cases, the best subsample of the reference dataset to satisfy such requirements. To this end, we introduce a new variable, expressing the desire to be exposed or not, and we set the question up as a model selection problem. The best model will be selected using the marginal probability of the responses and a suitable prior proposal over the model space. An application in the educational field is presented.