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 know 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 2dimensional 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.

A fast Monte Carlo test for preferential sampling

“…The biasing effects of PS on spatial prediction has been clearly demonstrated across a wide range of fields and can be severe in magnitude [Diggle et al, 2010, Watson et al, 2019b, Pennino et al, 2019, Dinsdale et al, 2019. Thus, PS should not be ignored in spatial analyses.…”

“…PS should also be considered in the analysis of environmental data recorded from tagged animals. Dinsdale et al [2019] demonstrated this with a case study using sea surface temperature recordings from tags attached to Elephant Seals in the Southern Indian ocean. The seals' preference for cooler waters led to biased 'naive' spatial estimates of sea surface temperature.…”

“…Next, Guan and Afshartous [2007] developed an alternative simulation-free test for PS. Instead of fitting a parametric model for the marks, their approach instead divides the region S into non over-lapping subregions.…”