This package present a general framework for detecting the preferential sampling in an environmental process across space and/or time.

This is based on the work A general theory for preferential sampling in environmental networks by Joe Watson, James V. Zidek and Gavin Shaddick. This is achieved by considering the joint distribution of an environmental process with a site-selection process that considers where and when sites are placed to measure the process. The environmental process may be spatial, temporal or spatio-temporal in nature. By sharing random effects between the two processes, the joint model is able to establish whether site placement was stochastically dependent of the environmental process under study.

The data are defined by a process indexed by space and time

$$ Y(s, t) = {y(s, t), (s, t) \in \mathcal{D} \subset \mathbb{R}^2\times \mathbb{R}} $$

and are observed at $n$ spatial locations or areas and at $T$ time points.

When considering the spatio-temporal data, we usually need to define a nonseparable spatio-temporal covariance function $cov(y(s_i, t), y(s_j, u))$. In practice, to overcome the computational complexity of the nonseparable models, we can simply assume separability so that the space-time covariance function is decomposed into the product of a purely spatial and a purely temporal term.