  We consider a multiple hypothesis testing problem in a sensor network over
the joint spatial-time domain. The sensor network is modeled as a graph, with
each vertex representing a sensor and a signal over time associated with each
vertex. We assume a hypothesis test and an associated p-value for every sample
point in the joint spatial-time domain. Our goal is to determine which points
have true alternative hypotheses. By parameterizing the unknown alternative
distribution of $p$-values and the prior probabilities of hypotheses being null
with a bandlimited generalized graph signal, we can obtain consistent estimates
for them. Consequently, we also obtain an estimate of the local false discovery
rates (lfdr). We prove that by using a step-up procedure on the estimated lfdr,
we can achieve asymptotic false discovery rate control at a pre-determined
level. Numerical experiments validate the effectiveness of our approach
compared to existing methods.
