MDBs Versus MIBs in Case of Multiple Hypotheses

Abstract

Statistical testing procedures employed in geodetic quality control often consist of two steps: detection and identification. In the detection step, the null hypothesis (working model) ℋ₀ undergoes a validity check. If the outcome of the detection step is the rejection of ℋ₀, identification of potential source of model error is exercised through a search among the specified alternative hypotheses. The testing performance is thus not only led by its ability to detect biases but to correctly identify them as well. The detection capability of a testing regime is usually assessed by its Minimal Detectable Bias (MDB) given a certain correct detection probability. The information provided by the MDB only concerns correct detection and not correct identification. The testing identification performance should be evaluated by its Minimal Identifiable Bias (MIB) given a certain correct identification probability. In this contribution, we demonstrate the difference between MDB and MIB. It is hereby highlighted that a small MDB (or a high probability of correct detection) does not necessarily imply a small MIB (or a high probability of correct identification). The factors driving the difference between detection and identification performance are illustrated using a simple example. Our analysis is then continued in the framework of deformation monitoring.