  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.
