## Variograms, Covariance functions and Stationarity

I just started a course on spatial statistics, so I’ve got covariance functions and variograms on the mind. This post is mostly for me to work through their intuition and relationship. Say you have some spatio-temporal process, with specific locations denoted , with the value of the process those points are . For concreteness, these locations could be latitude and longitude and the field could be the outdoor temperature. Or maybe the locations are the the space-time of a player on a basketball court and the field is her shot percentage or scoring efficiency from that point.