A Linear Regression Framework for the Verification of Bayesian Model Calibration Algorithms

Abstract

We describe a framework for the verification of Bayesian model calibration routines. The framework is based on linear regression and can be configured to verify calibration to data with a range of observation error characteristics. The framework is designed for efficient implementation and is suitable for verifying code intended for large-scale problems. We propose an approach for using the framework to verify Markov chain Monte Carlo (MCMC) software by combining it with a nonparametric test for distribution equality based on the energy statistic. Our matlab-based reference implementation of the framework is shown to correctly distinguish between output obtained from correctly and incorrectly implemented MCMC routines. Since correctness of output from an MCMC software depends on choosing settings appropriate for the problem-of-interest, our framework can potentially be used for verifying such settings.