DMS Statistics and Data Science Seminar

Speaker: Dr. Pulong Ma, Clemson University

Title: Beyond Matérn: On A Class of Interpretable Confluent Hypergeometric Covariance Functions

Abstract: In the past several decades, the Matérn covariance function has been a popular choice to model dependence structures in spatial statistics. A key benefit of the Matérn class is that it is possible to get precise control over the degree of differentiability of the process realizations. However, the Matérn class possesses exponentially decaying tails, and thus may not be suitable for modeling polynomial-tailed dependence. This problem can be remedied using polynomial covariances; however, one loses control over the degree of differentiability of the process realizations, in that the realizations using polynomial covariances are either infinitely differentiable or not differentiable at all. To overcome this dilemma, a new family of covariance functions is constructed using a scale mixture representation of the Matérn class where one obtains the benefits of both Matérn and polynomial covariances. The resultant covariance contains two parameters: one controls the degree of differentiability near the origin and the other controls the tail heaviness, independently of each other. The CH class also enjoys nice theoretical properties under infill asymptotics including equivalence measures, asymptotic behavior of the maximum likelihood estimators, and asymptotically efficient prediction under misspecified models. The improved theoretical properties in the predictive performance of the CH class are verified via extensive simulations. Application using OCO-2 data confirms the advantage of the CH class over the Matérn class, especially in extrapolative settings.