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It is of significant importance to provide network-wide Quality of Service (QoS) for a wide range of event detection applications in wireless sensor networks. This paper investigates the important problem of QoS provision to abnormal event detection. For event detection applications, there are two key performance metrics, i.e., detection probability and detection latency. This paper considers both metrics, aiming to provide statistical QoS for abnormal event detection. It is, however, a challenging issue because of stringent resource constraints of sensor nodes and unpredictable randomness of physical events. We propose a probabilistic approach to statistical QoS provision for event detection in sensor networks. We propose a distributed algorithm that iteratively determines the active probability of each sensor node. The probability is kept small for energy efficiency but sufficiently large to provide the required detection QoS. Our approach is flexible and can detection QoS customized by applications. Comprehensive simulation experiments have been conducted, which demonstrate that our approach is able to provide the required detection QoS for event detection and achieves considerably longer the system lifetime compared with other competing schemes. [ABSTRACT FROM AUTHOR]