Simulation-Based Calibration Checking for Bayesian Computation: The Choice of Test Quantities Shapes Sensitivity

Abstract

Simulation-based calibration checking (SBC) is a practical method to validate computationally-derived posterior distributions or their approximations. In this paper, we introduce a new variant of SBC to alleviate several known problems. Our variant allows the user to in principle detect any possible issue with the posterior, while previously reported implementations could never detect large classes of problems including when the posterior is equal to the prior. This is made possible by including additional data-dependent test quantities when running SBC. We argue and demonstrate that the joint likelihood of the data is an especially useful test quantity. Some other types of test quantities and their theoretical and practical benefits are also investigated. We provide theoretical analysis of SBC, thereby providing a more complete understanding of the underlying statistical mechanisms. We also bring attention to a relatively common mistake in the literature and clarify the difference between SBC and checks based on the data-averaged posterior. We support our recommendations with numerical case studies on a multivariate normal example and a case study in implementing an ordered simplex data type for use with Hamiltonian Monte Carlo. The SBC variant introduced in this paper is implemented in the $\mathtt{SBC}$ R package.

arXiv comment50 pages, 11 figures, upcoming in Bayesian Analysis

References in corpus (15)

• Rank-normalization, folding, and localization: An improved $\hat{R}$ for assessing convergence of MCMC
• Visualization in Bayesian workflow
• Validating Bayesian Inference Algorithms with Simulation-Based Calibration
• Graphical Test for Discrete Uniformity and its Applications in Goodness of Fit Evaluation and Multiple Sample Comparison
• Simulation-Based Calibration Checking for Bayesian Computation: The Choice of Test Quantities Shapes Sensitivity
• Intuitive Joint Priors for Bayesian Linear Multilevel Models: The R2D2M2 prior
• Diagnostics for Conditional Density Models and Bayesian Inference Algorithms
• GATSBI: Generative Adversarial Training for Simulation-Based Inference
• Calibration procedures for approximate Bayesian credible sets
• JANA: Jointly Amortized Neural Approximation of Complex Bayesian Models
• An Easy to Interpret Diagnostic for Approximate Inference: Symmetric Divergence Over Simulations
• AIDE: An algorithm for measuring the accuracy of probabilistic inference algorithms
• Testing whether a Learning Procedure is Calibrated
• A Family of Exact Goodness-of-Fit Tests for High-Dimensional Discrete Distributions
• Discovering Inductive Bias with Gibbs Priors: A Diagnostic Tool for Approximate Bayesian Inference

Cited by in corpus (5)

• Simulation-Based Calibration Checking for Bayesian Computation: The Choice of Test Quantities Shapes Sensitivity
• Uncertainty Quantification and Propagation in Surrogate-based Bayesian Inference
• Deep inference of simulated strong lenses in ground-based surveys
• Eliciting prior information from clinical trials via calibrated Bayes factor
• Gaussian distributional structural equation models: A framework for modeling latent heteroscedasticity