Presence-Only for Marked Point Process Under Preferential Sampling

Preferential sampling models have garnered significant attention in recent years. Although the original model was developed for geostatistics, it founds applications in other types of data, such as point processes in the form of presence-only data. While this has been recognized in the Statistics literature, there is value in incorporating ideas from both presence-only and preferential sampling literature. In this paper, we propose a novel model that extends existing ideas to handle a continuous variable collected through opportunistic sampling. To demonstrate the potential of our approach, we apply it to sardine biomass data collected during commercial fishing trips. While the data is intuitively understood, it poses challenges due to two types of preferential sampling: fishing events (presence data) are non-random samples of the region, and fishermen tend to set their nets in areas with a high quality and value of catch (i.e., bigger schools of the target species). We discuss theoretical and practical aspects of the problem, and propose a well-defined probabilistic approach. Our approach employs a data augmentation scheme that predicts the number of unobserved fishing locations and corresponding biomass (in kg). This allows for evaluation of the Poisson Process likelihood without the need for numerical approximations. The results of our case study may serve as an incentive to use data collected during commercial fishing trips for decision-making aimed at benefiting both ecological and economic aspects. The proposed methodology has potential applications in a variety of fields, including ecology and epidemiology, where marked point process model are commonly used.