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.