Multivariate spatial modelling through a convolution-based skewed process

  • Hamid Zareifard
  • Majid Jafari KhalediEmail author
  • Omar Dahdouh
Original Paper


In some statistical issues, several continuous spatial outcomes are simultaneously measured at each sampling location. In such circumstances, it is common to model the data through a multivariate Gaussian model. As the normality assumption is often untenable, this paper proposes a multivariate skewed spatial model which, by virtue of its capacity for capturing skewness, is potentially more flexible than symmetric ones. Specifically, a multivariate version of the Gaussian-log Gaussian convolution process is developed. The resulting covariance for the multivariate process is in general nonseparable. We also discuss the other properties of the induced covariance function. Furthermore, Markov chain Monte Carlo methods are used to make Bayesian inferences. The performance of the method is investigated through simulation experiments and by analyzing a real soil pollution dataset obtained from Golestan province, North of Iran.


Multivariate spatial data Non-Gaussian modelling Bayesian analysis Convolution Cross-dependency structure 



We thank two anonymous reviewers, the associate editor, and the editor for their constructive comments. Their very much precise comments have substantially improved the manuscript.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of StatisticsJahrom UniversityJahromIran
  2. 2.Department of StatisticsTarbiat Modares UniversityTehranIran

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