Multivariate confluent hypergeometric covariance functions with origin and tail flexibility

Music City Center 

Spatially-indexed multivariate data appear frequently in geostatistics and related fields including oceanography and environmental science, with data often modeled through covariance and cross-covariance functions in the Gaussian Process setting. The purpose of this work is to present techniques using multivariate mixtures for establishing validity that are simultaneously simplified and comprehensive. In particular, cross-covariances are constructed for the recently-introduced confluent hypergeometric (CH) class of covariance functions, which has slow (polynomial) decay in the tails of the covariance that better handles large gaps between observations in comparison with other covariance models. The approach leads to valid multivariate cross-covariance models that inherit the desired marginal properties of the confluent hypergeometric model and outperform the multivariate Matérn model in out-of-sample prediction under slowly-decaying correlation of the underlying multivariate random field. The model captures heavy tail decay and dependence between variables in an oceanography dataset of temperature, salinity and oxygen, as measured by autonomous floats in the Southern Ocean.

Cross-covariances

Multivariate geostatistics

Oceanography

Spectral construction 

Section on Statistics and the Environment