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Sensor networks (SNETs) for monitoring spatial phenomena has emerged as an area of significant practical interest. We focus on the important problem of detection of distributed events, sources, or abnormalities that are localized, i.e., only a small number of sensors in the vicinity of the phenomena are in the field of observation. This problem complements the standard decentralized detection problem, where noisy information about an event is measured by the entire network. For localized phenomena the main difficulty arises from the coupling of: a) noisy sensor observations that lead to local false positives/negatives; and b) limited energy, which constrains communication among sensor nodes. Together these difficulties call for reaching a decentralized statistical ordering based on limited collaboration. We are then led to the following fundamental problem: determine the most probable event locations while minimizing communication cost. Our objective in this paper is to characterize the fundamental trade offs between global performance (false alarms and miss rate) and communication cost. We develop a framework to minimize the communication cost subject to worst-case misclassification constraints by making use of the false discovery rate (FDR) concept along with an optimal local measure transformation at each sensor node. The preliminary results show that the FDR concept applied in a sensor networks context leads to significant reduction in the communication cost of the system. A very interesting implication of this work is that the detection performance of a wireless sensor network is comparable to that of a wired network of sensors.