Posterior SBC: Simulation-Based Calibration Checking Conditional on Data

TL;DR

This paper introduces posterior simulation-based calibration (SBC), a method for validating Bayesian inference algorithms conditioned on observed data, demonstrated through three diverse case studies.

Contribution

It proposes posterior SBC as a new approach to validate inference algorithms conditionally on observed data, extending traditional SBC methods.

Findings

Posterior SBC effectively detects calibration issues in various models.

The method is demonstrated on models including differential equations and neural network approximations.

Posterior SBC provides a practical validation tool for complex Bayesian models.

Abstract

Simulation-based calibration checking (SBC) refers to the validation of an inference algorithm and model implementation through repeated inference on data simulated from a generative model. In the original and commonly used approach, the generative model uses parameters drawn from the prior, and thus the approach is testing whether the inference works for simulated data generated with parameter values plausible under that prior. This approach is natural and desirable when we want to test whether the inference works for a wide range of datasets we might observe. However, after observing data, we are interested in answering whether the inference works conditional on that particular data. In this paper, we propose posterior SBC and demonstrate how it can be used to validate the inference conditionally on observed data. We illustrate the utility of posterior SBC in three case studies: (1) A simple multilevel model; (2) a model that is governed by differential equations; and (3) a joint integrative neuroscience model which is approximated via amortized Bayesian inference with neural networks.