Xuanlong Nguyen
University of Michigan

Simultaneous and sequential detection of
multiple interacting change points

Classical sequential analysis is concerned with optimal stopping rules for detecting a change point in the underlying distribution that generates a sequence of observations. It has become important in modeling and detecting faults in large distributed systems, such as sensor networks. But such systems in many situations present multiple interacting faults. For example, individual sensors in a network may fail and detection is performed by comparing measurements between sensors, resulting in statistical dependency among faults (change points). These situations require a new formulation of a sequential statistical decision problem extending the classical setup of sequential analysis. We present a new formulation for multiple interacting faults in a distributed system that includes specifications of how individual subsystems composing the large system may fail, the information that can be shared among these subsystems and the interaction pattern between faults. We propose a new sequential stopping algorithm for detecting multiple change points (faults). The main feature of the algorithm is that it uses composite stopping rules for a subsystem that depend on the decision of other subsystems. We will present an analysis of asymptotic false alarm and detection delay for this algorithm in a Bayesian setting and show that under certain conditions the proposed algorithm is optimal. The analysis methodology relies on elaborate comparison techniques between stopping times. We validate the analysis with some simulations.