Probabilities of Causation: Adequate Size of Experimental and Observational Samples

Ang Li, Ruirui Mao, Judea Pearl

Keywords: Probabilities of causation, Counterfactual, Structural causal model, Probability of necessity and sufficiency, Sample size

TL;DR: This paper talks about the adequate sample size to estimate the probabilities of causation.

Abstract: The probabilities of causation are commonly used to solve decision-making problems. Tian and Pearl derived sharp bounds for the probability of necessity and sufficiency (PNS), the probability of sufficiency (PS), and the probability of necessity (PN) using experimental and observational data. The assumption is that one is in possession of a large enough sample to permit an accurate estimation of the experimental and observational distributions. In this study, we present a method for determining the sample size needed for such estimation, when a given confidence interval (CI) is specified. We further show by simulation that the proposed sample size delivered stable estimations of the bounds of PNS.