A new model validation tool using kernel regression and density estimation.

Abstract

In physiological system modelling for control or decision support, model validation is a critical element. A nonparametric approach for assessing the validity of deterministic dynamic models against empirical data is developed, based on kernel regression and kernel density estimation, yielding visual graphical assessment tools as well as numerical metrics of compatibility between the model and the data. Nonparametric regression has been suggested for assessing a parametric statistical model by constructing a confidence band for the proposed model and then checking whether the nonparametric regression curve lies within the band. However, for deterministic models, there is no confidence band that can be constructed. A reversal of roles is therefore suggested--construct a probability band for the nonparametric regression curve and check whether the proposed model lies within the band. This approach extends the utility of nonparametric regression for model assessment to deterministic models. Weighted kernel density estimation is incorporated to derive a density profile for the regression curve, creating a local graphical validation tool. In addition, the density profile is used to define and compute two numerical measures--average normalized density (AND) and relative average normalized density (RAND), representing global statistical validity measures. These tools are demonstrated using a biomedical system model for agitation-sedation and sedation management control.