1. A method comprising: as new data points are added to a predefined streaming window of data points and as existing data points are removed from the streaming window, the streaming window being a temporal streaming window, each data point having a value for each dimension of a plurality of dimensions, each data point corresponding to a real world event of a same type, each dimension corresponding to a different real world property or characteristic related to the same type of the real world events to which the data points correspond, each time a given new data point is added to the streaming window or a given existing data point is removed from the streaming window, updating, by a processor of a computing device, a plurality of detection data structures without determining distances among the data points, each outlier detection data structure encompassing the data points within the streaming window for one corresponding dimension of the plurality of dimensions as opposed to for a combination of more than one corresponding dimension of the plurality of dimensions; and, using the outlier detection data structures to detect one or more outlier data points within the streaming window over selected one or more dimensions of the plurality of dimensions without determining distances among the data points, the outlier data points corresponding to real world events of particular interest.