Methods for preferential sampling in geostatistics

Preferential sampling in geostatistics occurs when the locations at which observations are made may depend on the spatial process that underlines the correlation structure of the measurements. If ignored, this may affect the parameter estimates of the model and the resulting spatial predictions. In this thesis, we first show that previously proposed Monte Carlo estimates for the likelihood function may not be approximating the desired function. Furthermore, we argue that for preferential sampling of moderate complexity, alternative and widely available numerical methods to approximate the likelihood function produce better results than Monte Carlo methods. We illustrate our findings on various data sets, include the biomonitoring Galicia dataset analysed previously in the literature. Research on preferential sampling has so far been restricted to stationary sampling locations such as monitoring sites. In this thesis, we also expand the methodology for applicability in cases where the sensors are moving through the domain of interest. 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 through a 2-dimensional space. The main application of these methods is the sampling of ocean temperature fields by marine mammal mounted sensors. This is an area of research which has grown drastically over the past 25 years and is providing scientists with a wealth of new oceanographic information in areas of our oceans previously not well understood. 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 ocean temperatures, hence resulting in a type of preferential sampling. 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. We apply our methods to sea surface temperature data collected by Southern elephant seals in the Southern Indian ocean and show how predictions of sea surface temperature fields using this data may vary when accounting for the preferential movement.