A correlated likelihood function for Bayesian model calibration to harness gradient information

Abstract

The problem of constitutive model calibration has traditionally been addressed using least squares-based curve-fitting approaches. In recent years, Bayesian approaches have been proposed to calibrate constitutive models with an eye on accounting for the variability in experimental data. Generally, the likelihood function in this approach focuses only on the data and any correlations between neighboring data-points are ignored. In this work, we demonstrate a straightforward approach to incorporating data correlations into the likelihood function that harnesses gradient information. This approach leads to improved fits and better identifiability of the constitutive model parameters.

Keywords:

• Constitutive modeling
• Bayesian likelihood
• data correlation
• soft tissue