Bayesian inference for spatial extremes under preferential sampling.

Music City Center 

In geostatistics, preferential sampling occurs when a location's inclusion probability correlates with the measured variable. For Gaussian spatial processes, preferential sampling has been shown to impact parameter estimation and degrade out-of-sample predictions. Most proposed solutions involve modeling the locations as a realization of a log Gaussian Cox process with the observed outcome as dependent on the same underlying spatial process. Preferentiality in non-Gaussian data is less explored. This study examines its impact on extremes, such as pollution or precipitation maxima. We introduce an intuitive modeling framework to induce a shared underlying spatial process between a location's maximum median value and its probability of being sampled, using the blended GEV distribution (bGEV). Inference is performed in a Bayesian framework, via an MCMC algorithm with a data augmentation step. We show how failing to account for preferentiality leads to biased parameter estimates, and how our solution improves inference compared to a baseline extremes spatial model. We apply our approach to estimate maxima of PM2.5 levels in California

preferential sampling, extremes, point process, log cox gaussian process

bayesian modeling 

Section on Statistics and the Environment