Metrics for bayesian optimal experiment design under model misspecification

Tommie Catanach, Niladri Das

Abstract:

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 Discrimi-
natory 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.