Data streams - data flows in which the information arrives in a timely manner - have recently become a major subfield of knowledge extraction. One of their most important singularity is that only a part of the information remains available at a time, which makes it necessary to cope with uncertainty. In this paper, we introduce a novel statistical approach which biases the initial support for patterns mining. This approach holds the advantage to maximize one of two parameters (precision or recall) chosen by the user, while guaranteeing a statistical near optimal degradation of the other. This leads us to introduce the statistical borders, the relevant sets of frequent patterns in incremental mining of data streams. Experiments performed on sequential patterns demonstrate the potential of this approach.