  This paper considers a problem of distributed hypothesis testing and social
learning. Individual nodes in a network receive noisy local (private)
observations whose distribution is parameterized by a discrete parameter
(hypotheses). The conditional distributions are known locally at the nodes, but
the true parameter/hypothesis is not known. An update rule is analyzed in which
nodes first perform a Bayesian update of their belief (distribution estimate)
of the parameter based on their local observation, communicate these updates to
their neighbors, and then perform a "non-Bayesian" linear consensus using the
log-beliefs of their neighbors. In this paper we show that under mild
assumptions, the belief of any node in any incorrect hypothesis converges to
zero exponentially fast, and we characterize the exponential rate of learning
which is given in terms of the network structure and the divergences between
the observations' distributions. Our main result is the concentration property
established on the rate of convergence.
