Baumgartner-Weiss-Schindler (BWS)

The Baumgartner-Weiss-Schindler test is a modern non-parametric test that combines advantages of several classical tests, with particular sensitivity to tail differences:

\[ B = \frac{1}{n_1 n_2} \sum_{i,j} \psi(F(x_i), F(y_j)) \]

where \(\psi\) is a weighting function that emphasizes tail regions.

Key characteristics:

  • Modern design: Developed to address limitations of classical tests

  • High power: Generally higher statistical power across various scenarios

  • Tail sensitivity: Strong sensitivity to tail differences like Anderson-Darling

  • Versatility: Performs well across different types of distributional shifts

When to use:

  • High-stakes computer vision (medical imaging, autonomous vehicles)

  • Production vision systems where missing drift is costly

  • When you need high statistical power across diverse drift scenarios

  • For detecting both location and scale shifts simultaneously

  • When computational cost is not a primary constraint

  • As a robust alternative when other tests give ambiguous results

Limitations:

Complexity and overhead. It is a more modern, complex statistic that is harder to find in standard libraries and may require more compute time for high-velocity data streams.