Matérn Covariance Function

The Matern covariance function is a covariance function used across spatial statistics, geostatistics, machine learning, and image analysis wherever a multivariate statistical model is built over a metric space. Named after the Swedish forestry statistician Bertil Matern, it specifies the covariance between two measurements purely as a function of the distance between the points at which they were taken. Because the covariance depends only on that distance rather than on the points' locations, the function is stationary, and when distance is measured in the ordinary Euclidean sense it is isotropic as well, meaning it looks the same in every direction.