## Optimal Spatial Prediction with Kriging

Suppose we are modeling a spatial process (for instance, the amount of rainfall around the world, the distribution of natural resources, or the population density of an endangered species). We’ve measured the latent function at some locations , and we’d like to predict the function’s value at some new location . Kriging is a technique for extrapolating our measurements to arbitrary locations. For an in-depth discussion, see Cressie and Wikle (2011). Here I derive Kriging in a simplified case. I will assume that is an intrinsically stationary process. In other words, there exists some semivariogram such that Furthermore, I will assume that the process is isotropic, (i.e. that is a function only of ). As Andy described here, the existence … Read More