Matern Correlation: A Panoramic Primer

Matern correlation is of pivotal importance in spatial statistics and machine learning. This paper serves as a panoramic primer for this correlation with an emphasis on the exposition of its changing behavior and smoothness properties in response to the change of its two parameters. Such exposition is achieved through a series of simulation studies, the use of an interactive 3D visualization applet, and a practical modeling example, all tailored for a wide-ranging statistical audience. Meanwhile, the thorough understanding of these parameter-smoothness relationships, in turn, serves as a pragmatic guide for researchers in their real-world modeling endeavors, such as setting appropriate initial values for these parameters and parameter-fine-tuning in their Bayesian modeling practice or simulation studies involving the Matern correlation. Derived problems surrounding Matern, such as inconsistent parameter inference, extended forms of Matern and limitations of Matern, are also explored and surveyed to impart a panoramic view of this correlation.