  Nonstationarity is a major challenge in analyzing spatial data. For example,
daily precipitation measurements may have increased variability and decreased
spatial smoothness in areas with high mean rainfall. Common nonstationary
covariance models introduce parameters specific to each location, giving a
highly-parameterized model which is difficult to fit. We develop a
nonstationary spatial model that uses the mean to determine the covariance in a
region, resulting in a far simpler, albeit more specialized, model. We explore
inferential and predictive properties of the model under various simulated data
situations. We show that this model in certain circumstances improves
predictions compared to a standard stationary spatial model. We further propose
a computationally efficient approximation that has comparable predictive
accuracy. We also develop a test for nonstationary data and show it reliably
identifies nonstationarity. We apply these methods to daily precipitation in
Puerto Rico.
