Bayesian feedback in the framework of ecological sciences

In ecological studies, it is not uncommon to encounter scenarios where the same phenomenon (e.g., species occurrence, species abundance) is observed using two different types of samplers. For example, species data can be collected from scientific sampling with a completely random sample pattern, but also from opportunistic sampling (e.g., whale watching from commercial fishing vessels or bird watching from citizen science), where observers tend to look for particular species in areas where they expect to find them. Species Distribution Models (SDMs) are widely used tools for analysing this type of ecological data. In particular, two models are available for the aforementioned data: a geostatistical model (GM) for data collected where the sampling design is not directly related to the observations, and a preferential model (PM) for data obtained from opportunistic sampling. The integration of information from disparate sources can be addressed through the use of expert elicitation and integrated models. This paper focuses on a sequential Bayesian procedure for linking two models by updating prior distributions. The Bayesian paradigm is implemented together with the integrated nested Laplace approximation (INLA) methodology, which is an effective approach for making inference and predictions in spatial models with high performance and low computational cost. This sequential approach has been evaluated through the simulation of various scenarios and the subsequent comparison of the results from sharing information between models using a variety of criteria. The procedure has also been exemplified on a real dataset. The primary findings indicate that, in general, it is preferable to transfer information from the independent (with a completely random sampling) model to the preferential model rather than in the alternative direction. However, this depends on several factors, including the spatial range and the spatial arrangement of the sampling locations.