Evaluation of a soil greenhouse gas emission model based on Bayesian inference and MCMC: Parameter identifiability and equifinality

Abstract

Identifiability and equifinality are two interrelated concepts in mathematical modeling. The derivation of the Hessian matrix becomes crucial when the condition number is used as a diagnostic indicator for identifiability. The covariance-inverse (CI) method was proposed to derive the Hessian matrix via the inverse matrix of covariance. The covariance matrix is calculated directly from the posterior parameter samples. Compared with two existing methods, i.e., difference quotients (DQ) and quasi-analytical (QA), CI is more efficient and reliable. The CI method was then used for identifiability diagnosis on a soil greenhouse gas emission (SoilGHG) model. The model as a whole was poorly identified, but a reduced model with fewer parameters could become identifiable, which is called “conditionally identifiable” in this paper. The geometric mean condition numbers in terms of sorted singular values of the full Hessian matrix could be adopted as criteria to determine at most how many undetermined parameters might be included in an identifiable or weakly identifiable model. The combinations of parameters that made the model identifiable were also determined by the proposed diagnosis method. We addressed the importance of understanding both identifiability and equifinality in ecosystem modeling.