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An outage detection framework for power distribution networks is proposed. Given the tree structure of a distribution system, a detection method is developed combining the use of realtime power flow measurements on the edges of the tree with load forecasts at the nodes of the tree. The maximum likelihood detection decision for an arbitrary number of outages is shown to be efficiently computable due to decoupling across local areas determined by the sensor locations. To minimize the maximum missed detection probability, the optimal sensor placement is efficiently computed as well. Finally, a set of case studies is conducted using feeder data from the Pacific Northwest National Laboratories. It is shown that 10% mean detection error probability can be achieved by a sensor density of 30% for a typical feeder with the proposed optimal sensor placement and outage detection methods.