The need for improving the capability to detect illegal or hazardous activities and yet reducing the workload of operators involved in various surveillance tasks calls for research on more capable automatic tools. To maximize their performance, these tools should be able to combine automatic capturing of normal behavior from data with domain knowledge in the form of human descriptions. In a proposed Joint Statistical and Symbolic Anomaly Detection System, statistical and symbolic methods are tightly integrated in order to detect the majority of critical events in the situation while minimizing unwanted alerts. We exemplify the proposed system in the domain of maritime surveillance.