Correlation of parameter estimators for models admitting multiple parametrizations

Abstract

When estimating parameters using noisy data, uncertainty quantification methods provide a way to investigate the confidence one has in the parameter estimates, as well as to obtain information on the possible dependence of parametric estimators on one another. In this note, we consider uncertainty quantification techniques that allow visualization of the distributions of these parameter estimators for evidence of possible correlation. We consider three mathematical models (the logistic curve, the Richards curve, and the spring equation), which permit multiple parametrizations, and compare the corresponding parameter estimators for possible dependence/independence. The uncertainty quantification techniques we employ include the correlation coefficients, asymptotic as well as exact confidence regions or ellipsoids, and Monte Carlo plots generated by the DRAM algorithm.