  This paper studies the problem of sequential Gaussian shift-in-mean
hypothesis testing in a distributed multi-agent network. A sequential
probability ratio test (SPRT) type algorithm in a distributed framework of the
\emph{consensus}+\emph{innovations} form is proposed, in which the agents
update their decision statistics by simultaneously processing latest
observations (innovations) sensed sequentially over time and information
obtained from neighboring agents (consensus). For each pre-specified set of
type I and type II error probabilities, local decision parameters are derived
which ensure that the algorithm achieves the desired error performance and
terminates in finite time almost surely (a.s.) at each network agent. Large
deviation exponents for the tail probabilities of the agent stopping time
distributions are obtained and it is shown that asymptotically (in the number
of agents or in the high signal-to-noise-ratio regime) these exponents
associated with the distributed algorithm approach that of the optimal
centralized detector. The expected stopping time for the proposed algorithm at
each network agent is evaluated and is benchmarked with respect to the optimal
centralized algorithm. The efficiency of the proposed algorithm in the sense of
the expected stopping times is characterized in terms of network connectivity.
Finally, simulation studies are presented which illustrate and verify the
analytical findings.
