Network traffic classification that is widely applicable and highly accurate is valuable for many network security and management tasks. A flexible and easily configurable classification framework is ideal, as it can be customized for use in a wide variety of networks. In this paper, we propose a highly configurable and flexible machine learning traffic classification method that relies only on statistics of sequences of packets to distinguish known, or approved, traffic from unknown traffic. Our method is based on likelihood estimation, provides a measure of certainty for classification decisions, and can classify traffic at adjustable certainty levels. Our classification method can also be applied in different classification scenarios, each prioritizing a different classification goal. We demonstrate how our classification scheme and all its configurations perform well on real-world traffic from a high performance computing network environment.