A Simulation-Based Test of Identifiability for Bayesian Causal Inference

This paper introduces a procedure for testing the identifiability of Bayesian models for causal inference. Although the do-calculus is sound and complete given a causal graph, many practical assumptions cannot be expressed in terms of graph structure alone, such as the assumptions required by instrumental variable designs, regression discontinuity designs, and within-subjects designs. We present simulation-based identifiability (SBI), a fully automated identification test based on a particle optimization scheme with simulated observations. This approach expresses causal assumptions as priors over functions in a structural causal model, including flexible priors using Gaussian processes. We prove that SBI is asymptotically sound and complete, and produces practical finite-sample bounds. We also show empirically that SBI agrees with known results in graph-based identification as well as with widely-held intuitions for designs in which graph-based methods are inconclusive.