Modelling ocean temperatures from bio-probes under preferential sampling

Abstract

In the last 25 years there has been an important increase in the amount of data collected from animal-mounted sensors (bio-probes), which are often used to study the animals' behaviour or environment. We focus here on an example of the latter, where the interest is in sea surface temperature (SST), and measurements are taken from sensors mounted on Elephant Seals in the Southern Indian ocean. We show that standard geostatistical models may not be reliable for this type of data, due to the possibility that the regions visited by the animals may depend on the SST. This phenomenon is known in the literature as preferential sampling, and, if ignored, it may affect the resulting spatial predictions and parameter estimates. Research on this topic has been mostly restricted to stationary sampling locations such as monitoring sites. The main contribution of this manuscript is to extend this methodology to observations obtained by devices that move through the region of interest, as is the case with the tagged seals. More specifically, we propose a flexible framework for inference on preferentially sampled fields, where the process that generates the sampling locations is stochastic and moving over time through a 2-dimensional space. Our simulation studies confirm that predictions obtained from the preferential sampling model are more reliable when this phenomenon is present, and they compare very well to the standard ones when there is no preferential sampling. Finally, we note that the conclusions of our analysis of the SST data can change considerably when we incorporate preferential sampling in the model.