  This paper addresses the challenges of optimally placing a finite number of
sensors to detect Poisson-distributed targets in a bounded domain. We seek to
rigorously account for uncertainty in the target arrival model throughout the
problem. Sensor locations are selected to maximize the probability that no
targets are missed. While this objective function is well-suited to
applications where failure to detect targets is highly undesirable, it does not
lead to a computationally efficient optimization problem. We propose an
approximation of the objective function that is non-negative, submodular, and
monotone and for which greedy selection of sensor locations works well. We also
characterize the gap between the desired objective function and our
approximation. For numerical illustrations, we consider the case of the
detection of ship traffic using sensors mounted on the seafloor.
