Bayesian feedback in the framework of ecological sciences

In ecology we may find scenarios where the same phenomenon (species occurrence, species abundance, etc.) is observed using two different types of samplers. For instance, species data can be collected from scientific sampling with a completely random sample pattern, but also from opportunistic sampling (e.g., whale or bird watching fishery commercial vessels), in which observers tend to look for a specific species in areas where they expect to find Species Distribution Models (SDMs) are a widely used tool for analyzing this kind of ecological data. Specifically, we have two models available for the above data: a geostatistical model (GM) for the data coming from a complete random sampler and a preferential model (PM) for data from opportunistic sampling. Integration of information coming from different sources can be handled via expert elicitation and integrated models. We focus here in a sequential Bayesian procedure to connect two models through the update of prior distributions. Implementation of the Bayesian paradigm is done through the integrated nested Laplace approximation (INLA) methodology, a good option to make inference and prediction in spatial models with high performance and low computational costs. This sequential approach has been evaluated by simulating several scenarios and comparing the results of sharing information from one model to another using different criteria. The procedure has also been exemplified with a real dataset. Our main results imply that, in general, it is better to share information from the independent (completely random) to the preferential model than the alternative way. However, it depends on different factors such as the spatial range or the spatial arrangement of sampling locations.