Illegal, Unreported and Unregulated (IUU) fishing activities pose one of the most significant threats to sustainable fisheries worldwide. Identifying illegal behaviour, specifically fishing and at-sea transhipment, continues to be a fundamental hurdle in combating IUU fishing. Here, we explore the use of spatial statistical methods to identify vessels behaving anomalously, in particular with regard to loitering, using the Indonesian Exclusive Economic Zone (EEZ) and surrounding waters as a case-study. Using Automatic Identification System (AIS) for vessel tracking, we applied Generalized Additive Models to capture both the temporal and spatial nature of loitering behaviour. We identified three statistically anomalous loitering behaviours (based on time, speed and distance) and applied the models to 2700 vessels in the region. We were able to rank vessels for individual and joint probability of atypical behaviour, providing a hierarchical list of vessels engaging in anomalous behaviour. While identification of irregular behaviour does not mean vessels are definitely engaging in illegal activities, this statistical modelling approach can be used to prioritise the allocation of enforcement resources and assist authorities under the United Nations Food and Agricultural Organization Port State Measures Agreement for management and enforcement of IUU fishing associated activities.