Parallel Mixture Procedure for Multi-Sensor Change-Point Detection

• Activity Number: 620
• Type: Contributed
• Date/Time: Thursday, August 2, 2012 : 8:30 AM to 10:20 AM
• Sponsor: IMS
• Author(s): Yao Xie*+ and David Oliver Siegmund
• Companies: Duke University and Stanford University
• Keywords: Change-point detection ; Sequential detection ; High-dimensional problem ; Time series ; Sensor network ; quality control

Abstract

We develop a parallel mixture procedure for multi-sensor sequential change-point detection, where sensors are distributed to monitor the emergence of a signal that changes the means of observations for an unknown subset of sensors. An empirical observation is that the fraction of affected sensors, p, is usually small. To exploit this sparsity, in our earlier work, we proposed a mixture procedure by assuming that each sensor has a chance p0 to be affected by the change-point. The value of p0 is a guess for p. We showed that the mixture procedure has better performance than existing procedures in literature; however, it may be sensitive to a mis-specification of p0. To achieve robustness over a wider range of p, we consider a parallel mixture procedure that combines several mixture procedures, each using a different parameter p0 and monitoring a different range of p values. We present a theoretical approximation to the average-run-length (ARL) of the parallel procedure which can be used to determine the thresholds efficiently. We show that the parallel mixture procedure has a smaller expected detection delay than a single mixture procedure over a wide range of p values.