Probabilities of Causation: Role of Observational Data

TL;DR

This paper explores how observational data can improve bounds on probabilities of causation, detailing conditions for their usefulness and quantifying potential improvements in decision-making scenarios.

Contribution

It introduces conditions under which observational data enhance bounds on causation probabilities and quantifies expected improvements assuming uniform distribution of observational data.

Findings

Observational data can improve bounds under specific conditions.

Expected improvement of bounds is quantifiable assuming uniform distribution.

Application to unit selection problem demonstrates practical relevance.

Abstract

Probabilities of causation play a crucial role in modern decision-making. Pearl defined three binary probabilities of causation, the probability of necessity and sufficiency (PNS), the probability of sufficiency (PS), and the probability of necessity (PN). These probabilities were then bounded by Tian and Pearl using a combination of experimental and observational data. However, observational data are not always available in practice; in such a case, Tian and Pearl's Theorem provided valid but less effective bounds using pure experimental data. In this paper, we discuss the conditions that observational data are worth considering to improve the quality of the bounds. More specifically, we defined the expected improvement of the bounds by assuming the observational distributions are uniformly distributed on their feasible interval. We further applied the proposed theorems to the unit selection problem defined by Li and Pearl.