  Clustered effects are often encountered in multiple hypothesis testing of
spatial signals. In this paper, we propose a new method, termed two-dimensional
spatial multiple testing (2d-SMT) procedure, to control the false discovery
rate (FDR) and improve the detection power by exploiting the spatial
information encoded in neighboring observations. The proposed method provides a
novel perspective of utilizing spatial information by gathering signal patterns
and spatial dependence into an auxiliary statistic. 2d-SMT rejects the null
when a primary statistic at the location of interest and the auxiliary
statistic constructed based on nearby observations are greater than their
corresponding thresholds. 2d-SMT can also be combined with different variants
of the weighted BH procedures to improve the detection power further. A fast
step-down algorithm is developed to accelerate the search for optimal
thresholds in 2d-SMT. In theory, we establish the asymptotical FDR control of
2d-SMT under weak spatial dependence. Extensive numerical experiments
demonstrate that the 2d-SMT method combined with various weighted BH procedures
achieves the most competitive performance in FDR and power trade-off.
