Detection-only versus detection and identification of model misspecifications

Abstract

It is common practice to use the well-known concept of the minimal detectable bias (MDB) to assess the performance of statistical testing procedures. However, such procedures are usually applied to a null and a set of multiple alternative hypotheses with the aim of selecting the most likely one. Therefore, in the DIA method for the detection, identification and adaptation of model misspecifications, rejection of the null hypothesis is followed by identification of the potential source of the model misspecification. With identification included, the MDBs do not truly reflect the capability of the testing procedure and should therefore be replaced by the minimal identifiable bias (MIB). In this contribution, we analyse the MDB and the MIB, highlight their differences, and describe their impact on the nonlinear DIA-estimator of the model parameters. As the DIA-estimator inherits all the probabilistic properties of the testing procedure, the differences in the MDB and MIB propagation will also reveal the different consequences a detection-only approach has versus a detection+identification approach. Numerical algorithms are presented for computing the MDB and the MIB and also their effect on the DIA-estimator. These algorithms are then applied to a number of examples so as to analyse and illustrate the different concepts.