SBI: A Simulation-Based Test of Identifiability for Bayesian Causal Inference
This provides a practical tool for researchers in causal inference to assess identifiability in complex models, though it is incremental as it builds on existing Bayesian approaches.
The paper tackles the problem of testing identifiability in Bayesian causal inference models, which are often analytically intractable, by introducing simulation-based identifiability (SBI), a procedure that uses particle-based optimization on simulated data to determine identifiability, and shows empirical agreement with known results on benchmarks.
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.