SBI: A Simulation-Based Test of Identifiability for Bayesian Causal Inference

TL;DR

This paper introduces simulation-based identifiability (SBI), a method to test whether causal queries are identifiable in Bayesian models implemented as probabilistic programs, complementing analytical methods.

Contribution

The paper presents SBI, a novel simulation-based procedure for testing identifiability in Bayesian causal inference models, including those intractable analytically.

Findings

SBI is sound for a broad class of probabilistic programs.

Empirical validation shows SBI agrees with known identification results.

SBI effectively handles complex models like Gaussian processes.

Abstract

A growing family of approaches to causal inference rely on Bayesian formulations of assumptions that go beyond causal graph structure. For example, Bayesian approaches have been developed for analyzing instrumental variable designs, regression discontinuity designs, and within-subjects designs. This paper introduces simulation-based identifiability (SBI), a procedure for testing the identifiability of queries in Bayesian causal inference approaches that are implemented as probabilistic programs. SBI complements analytical approaches to identifiability, leveraging a particle-based optimization scheme on simulated data to determine identifiability for analytically intractable models. We analyze SBI's soundness for a broad class of differentiable, finite-dimensional probabilistic programs with bounded effects. Finally, we provide an implementation of SBI using stochastic gradient descent, and show empirically that it agrees with known identification results on a suite of graph-based and quasi-experimental design benchmarks, including those using Gaussian processes.