Metrics for Bayesian Optimal Experiment Design Under Model Misspecification

The conventional approach to Bayesian decision-theoretic experiment design involves searching over possible experiments to select a design that maximizes the expected value of a specified utility function. The expectation is over the joint distribution of all unknown variables implied by the statistical model that will be used to analyze the collected data. Utility functions define experiments' objectives; a common utility function is information gain. This article introduces an expanded framework for experimental design, where we go beyond the traditional Expected Information Gain criteria. We introduce Expected General Information Gain which measures robustness to the model discrepancy, and Expected Discriminatory Information to quantify how well an experiment can detect model discrepancy. The functionality of the framework is showcased through its application to a scenario involving a linearized spring mass damper system and an F-16 model where the model discrepancy is taken into account while doing Bayesian optimal experiment design.