Analyses of the Impact of Different Types of Acceptance Regions on Data Snooping with Multiple Alternative Hypotheses

Objectives: When the a priori variance factor is known, hyperellipsoidal or hyperpolyhedral acceptance regions are frequently utilized for data snooping with multiple alternative hypotheses to pinpoint potential outliers in the observations. Despite their prevalence, there is a dearth of research examining how these regions affect the efficacy of data snooping. Methods: This study employs residual- and misclosurebased Baarda w-test statistics to provide a comprehensive analysis of the impact of different acceptance regions on the testing space, decision probabilities, the minimal detectable bias (MDB), and the probability of correctly identifying an alternative hypothesis. It also explores how the geometry of the functional model impacts the correct identification probabilities in a two-dimensional misclosure-based testing space. Results: The results show that different types of acceptance regions have a certain impact on the size of the MDB and the testing decision probabilities, but it is not significant. However, under certain geometric conditions, the variation in correct identification probabilities is significant, with a theoretical difference of nearly 3% in single-point positioning scenarios. From the geometric perspective of partitioning of the misclosure space, the difference in acceptance regions will change the subspaces of the critical regions, thereby affecting the results of outlier detection and identification. Conclusions: Analyzing the relationship between different types of acceptance regions and model geometry can help improve the model geometry and reduce its impact on the probability of correct identification. The findings of this research are informative for the selection of hyperellipsoid and hyperpolyhedral acceptance regions, when employing data snooping with multiple alternative hypotheses in scenarios where the a priori variance factor is known.