Title: Demonstration of the Relationship between Sensitivity and Identifiability for Inverse Uncertainty Quantification,
Abstract: Inverse Uncertainty Quantification (UQ), or Bayesian calibration, is the
process to quantify the uncertainties of random input parameters based on
experimental data. The introduction of model discrepancy term is significant
because "over-fitting" can theoretically be avoided. But it also poses
challenges in the practical applications. One of the mostly concerned and
unresolved problem is the "lack of identifiability" issue. With the presence of
model discrepancy, inverse UQ becomes "non-identifiable" in the sense that it
is difficult to precisely distinguish between the parameter uncertainties and
model discrepancy when estimating the calibration parameters. Previous research
to alleviate the non-identifiability issue focused on using informative priors
for the calibration parameters and the model discrepancy, which is usually not
a viable solution because one rarely has such accurate and informative prior
knowledge. In this work, we show that identifiability is largely related to the
sensitivity of the calibration parameters with regards to the chosen responses.
We adopted an improved modular Bayesian approach for inverse UQ that does not
require priors for the model discrepancy term. The relationship between
sensitivity and identifiability was demonstrated with a practical example in
nuclear engineering. It was shown that, in order for a certain calibration
parameter to be statistically identifiable, it should be significant to at
least one of the responses whose data are used for inverse UQ. Good
identifiability cannot be achieved for a certain calibration parameter if it is
not significant to any of the responses. It is also demonstrated that "fake
identifiability" is possible if model responses are not appropriately chosen,
or inaccurate but informative priors are specified.