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

arXiv: https://arxiv.org/abs/2102.11761 · HTML: https://mlsanity.com/paper/2102.11761/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 56 references that are in the map.
- First posted on arXiv 23 Feb 2021.

## Builds on (most cited first, 17 of 17)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Causal Effect Inference with Deep Latent-Variable Models](https://mlsanity.com/paper/1705.08821/) (2017)
- [Pyro: Deep Universal Probabilistic Programming](https://mlsanity.com/paper/1810.09538/) (2018)
- [Validating Bayesian Inference Algorithms with Simulation-Based Calibration](https://mlsanity.com/paper/1804.06788/) (2018)
- [Probabilities of Causation: Bounds and Identification](https://mlsanity.com/paper/1301.3898/) (2013)
- [Counterfactual Probabilities: Computational Methods, Bounds and Applications](https://mlsanity.com/paper/1302.6784/) (2013)
- [Interval Estimation of Individual-Level Causal Effects Under Unobserved Confounding](https://mlsanity.com/paper/1810.02894/) (2018)
- [A Critical Look at the Consistency of Causal Estimation With Deep Latent Variable Models](https://mlsanity.com/paper/2102.06648/) (2021)
- [Venture: a higher-order probabilistic programming platform with programmable inference](https://mlsanity.com/paper/1404.0099/) (2014)
- [Flexible sensitivity analysis for observational studies without observable implications](https://mlsanity.com/paper/1809.00399/) (2018)
- [Implicit Causal Models for Genome-wide Association Studies](https://mlsanity.com/paper/1710.10742/) (2017)
- [Causal Inference using Gaussian Processes with Structured Latent Confounders](https://mlsanity.com/paper/2007.07127/) (2020)
- [Efficient Identification in Linear Structural Causal Models with Instrumental Cutsets](https://mlsanity.com/paper/1910.13493/) (2019)
- [A Nonparametric Bayesian Methodology for Regression Discontinuity Designs](https://mlsanity.com/paper/1704.04858/) (2017)
- [MultiVerse: Causal Reasoning using Importance Sampling in Probabilistic Programming](https://mlsanity.com/paper/1910.08091/) (2019)
- [Bayesian causal inference via probabilistic program synthesis](https://mlsanity.com/paper/1910.14124/) (2019)

## Built on by (most cited first, 3 of 3)

- [Neural Causal Models for Counterfactual Identification and Estimation](https://mlsanity.com/paper/2210.00035/) (2022)
- [Counterfactual Identifiability of Bijective Causal Models](https://mlsanity.com/paper/2302.02228/) (2023)
- [Counterfactual (Non-)identifiability of Learned Structural Causal Models](https://mlsanity.com/paper/2301.09031/) (2023)

## Abstract (arXiv)

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.