# EM-algorithm for spatial data

I am very new to Geostatistics (Modeling spatial data) and have some questions:

1- I found that in many literature, the spatial random field is divided into spatial bins. That is, suppose I am interesting in Modeling the zinc concentration measured at different locations. Then, we measure the distance between all pair of locations. After that, we divide the observations into spatial lags based on the distance between them. For example, the first lag contains the pair of locations that there spatial distance between them is 10 meters, and so on. My question is, why we should do this step?

2- Can we fit a Gaussian mixture model using EM to the data without dividing them into spatial bin?

1- If I understand correctly, what you are referring to here is data discretization: in your example, instead of representing the concentration of zinc as a continuous function of the position (left - I assumed a concentration represented over a 1D line, although I guess your data are represented on a 2D map), you would bin them to obtain a discrete distribution (right). In the later case, the first bin represents the concentration of zinc in the $$[0m-10m]$$ segment, the second bin represents the concentration of zinc in the $$]10m-20m]$$ segment, and so on. The goal of discretization is generally to simplify your data for visualization, e.g. to be able to represent them using an histogram as on the right figure.