Sequential Nonparametric Tests for a Change in Distribution: An Application to Detecting Radiological Anomalies

ABSTRACT

We propose a sequential nonparametric test for detecting a change in distribution, based on windowed Kolmogorov–Smirnov statistics. The approach is simple, robust, highly computationally efficient, easy to calibrate, and requires no parametric assumptions about the underlying null and alternative distributions. We show that both the false-alarm rate and the power of our procedure are amenable to rigorous analysis, and that the method outperforms existing sequential testing procedures in practice. We then apply the method to the problem of detecting radiological anomalies, using data collected from measurements of the background gamma-radiation spectrum on a large university campus. In this context, the proposed method leads to substantial improvements in time-to-detection for the kind of radiological anomalies of interest in law-enforcement and border-security applications.Supplementary materials for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement.

Keywords:

• Anomaly detection
• Kolmogorov–Smirnov test
• Radiological survey
• Sequential testing