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25 Simulation-Based Calibration

A Bayesian posterior is calibrated if the posterior intervals have appropriate coverage. For example, 80% intervals are expected to contain the true parameter 80% of the time. If data is generated according to a model, Bayesian posterior inference with respect to that model is calibrated by construction. Simulation-based calibration (SBC) exploits this property of Bayesian inference to asses the soundness of a posterior sampler. Roughly, the way it works is by simulating parameters according to the prior, then simulating data conditioned on the simulated parameters, then testing posterior calibration of the inference algorithm over independently simulated data sets. This chapter follows Talts et al. (2018), which improves on the original approach developed by Cook, Gelman, and Rubin (2006).


Cook, Samantha R., Andrew Gelman, and Donald B Rubin. 2006. “Validation of Software for Bayesian Models Using Posterior Quantiles.” Journal of Computational and Graphical Statistics 15 (3): 675–92.

Talts, Sean, Michael Betancourt, Daniel Simpson, Aki Vehtari, and Andrew Gelman. 2018. “Validating Bayesian Inference Algorithms with Simulation-Based Calibration.” arXiv, no. 1804.06788.