2 research outputs found
A Generalized Bayesian Approach to Model Calibration
In model development, model calibration and validation play complementary
roles toward learning reliable models. In this article, we expand the Bayesian
Validation Metric framework to a general calibration and validation framework
by inverting the validation mathematics into a generalized Bayesian method for
model calibration and regression. We perform Bayesian regression based on a
user's definition of model-data agreement. This allows for model selection on
any type of data distribution, unlike Bayesian and standard regression
techniques, that "fail" in some cases. We show that our tool is capable of
representing and combining least squares, likelihood-based, and Bayesian
calibration techniques in a single framework while being able to generalize
aspects of these methods. This tool also offers new insights into the
interpretation of the predictive envelopes (also known as confidence bands)
while giving the analyst more control over these envelopes. We demonstrate the
validity of our method by providing three numerical examples to calibrate
different models, including a model for energy dissipation in lap joints under
impact loading. By calibrating models with respect to the validation metrics
one desires a model to ultimately pass, reliability and safety metrics may be
integrated into and automatically adopted by the model in the calibration
phase