Kriging with trend functions nonlinear in their parameters: Theory and application in enzyme kinetics

Kriging is an interpolation method commonly applied in empirical modeling for approximating functional relationships between impact factors and system response. The interpolation is based on a statistical analysis of given data and can optionally include a priori defined trend functions. However, Kriging can so far only be used with trend functions that are linear with respect to the parameters. In this contribution, we present an extension of the Kriging approach for handling trend functions that are nonlinear in their parameters. Our approach is based on Taylor linearization combined with an iterative parameter estimation procedure whose solution is practically computed via a root finding problem. We demonstrate our novel approach with measurement data from the application field of biocatalysis.