Improving identifiability in model calibration using multiple responses

In physics-based engineering modeling, the two primary sources of model uncertainty, which account for the differences between computer models and physical experiments, are parameter uncertainty and model discrepancy. Distinguishing the effects of the two sources of uncertainty can be challenging. For situations in which identifiability cannot be achieved using only a single response, we propose to improve identifiability by using multiple responses that share a mutual dependence on a common set of calibration parameters. To that end, we extend the single response modular Bayesian approach for calculating posterior distributions of the calibration parameters and the discrepancy function to multiple responses. Using an engineering example, we demonstrate that including multiple responses can improve identifiability (as measured by posterior standard deviations) by an amount that ranges from minimal to substantial, depending on the characteristics of the specific responses that are combined.