Counterfactual Probabilities: Computational Methods, Bounds and Applications

TL;DR

This paper develops computational methods for evaluating counterfactual probabilities, providing bounds when causal mechanisms are partially known, and demonstrates their application in treatment efficacy and liability assessment.

Contribution

It introduces techniques for computing bounds on counterfactual probabilities from observable data and applies them to real-world problems like treatment evaluation and legal liability.

Findings

Exact evaluation possible with known causal mechanisms

Bounds can be computed from observational data when mechanisms are unknown

Applications demonstrated in treatment efficacy and liability cases

Abstract

Evaluation of counterfactual queries (e.g., "If A were true, would C have been true?") is important to fault diagnosis, planning, and determination of liability. In this paper we present methods for computing the probabilities of such queries using the formulation proposed in [Balke and Pearl, 1994], where the antecedent of the query is interpreted as an external action that forces the proposition A to be true. When a prior probability is available on the causal mechanisms governing the domain, counterfactual probabilities can be evaluated precisely. However, when causal knowledge is specified as conditional probabilities on the observables, only bounds can computed. This paper develops techniques for evaluating these bounds, and demonstrates their use in two applications: (1) the determination of treatment efficacy from studies in which subjects may choose their own treatment, and (2) the determination of liability in product-safety litigation.