  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.
