Separability Analysis for Baarda Data Snooping Method

Abstract:

The Baarda’ data snooping method detects the outlier by making decision between the null and alternative hypotheses. Based on this method, usually only the false alert and missed detection were considered and the possibilities were defined for the minimal detectable bias (MDB). Nevertheless, in practical application, there are always multiple alternative hypotheses. Therefore, a third type error  wrong exclusion  occurs, which was caused by the correlation between two test statistics. The probabilities of false alert, missed detection, wrong exclusion can be considered as functions of the correlation coefficient. Monte Carlo methods were used to calculate the possibilities of these three types of errors with different correlation coefficients for two alternative hypotheses. It has proved that when the correlation is high the probability of committing wrong exclusion increases exponentially. As a result, the discrepancy between the theoretical and realistic MDB values enlarges, and accordingly the confidence level and the system reliability decrease. Finally, numerical experiments were conducted to analyze and compare the performance of two examples with different geometry conditions.

Key words:data snooping; wrong exclusion; test statistic; correlation coefficient