  This work analyzes the asymptotic performances of fully distributed
sequential hypothesis testing procedures as the type-I and type-II error rates
approach zero, in the context of a sensor network without a fusion center. In
particular, the sensor network is defined by an undirected graph, where each
sensor can observe samples over time, access the information from the adjacent
sensors, and perform the sequential test based on its own decision statistic.
Different from most literature, the sampling process and the information
exchange process in our framework take place simultaneously (or, at least in
comparable time-scales), thus cannot be decoupled from one another. Two
message-passing schemes are considered, based on which the distributed
sequential probability ratio test (DSPRT) is carried out respectively. The
first scheme features the dissemination of the raw samples. Although the sample
propagation based DSPRT is shown to yield the asymptotically optimal
performance at each sensor, it incurs excessive inter-sensor communication
overhead due to the exchange of raw samples with index information. The second
scheme adopts the consensus algorithm, where the local decision statistic is
exchanged between sensors instead of the raw samples, thus significantly
lowering the communication requirement compared to the first scheme. In
particular, the decision statistic for DSPRT at each sensor is updated by the
weighted average of the decision statistics in the neighbourhood at every
message-passing step. We show that, under certain regularity conditions, the
consensus algorithm based DSPRT also yields the order-2 asymptotically optimal
performance at all sensors.
