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Ph.d. forelæsning/PhD Defense - Francisco Cuevas


10.05.2019 kl. 13.00 - 16.00


Second order moment properties of point processes and random fields defined on a Euclidean space, a sphere, or the product of such spaces

The thesis is focused on second order moment properties for random fields and point processes on a Euclidean space, a sphere or the product of such spaces. This thesis consists of six research papers. Publication A criticizes the Gneiting covariance function family and provides conditions such that this family yields a covariance functions with a counterintuitive statistical meaning. Publication B presents a family of covariance functions for geostatistical data collected on the sphere, capable of modeling the degree of smoothness in the mean{squared sense.

Publication C shows a fast and exact algorithm to simulate random fields on a sphere or the product of the sphere times the Euclidean space. Publication D gives an extension of the K{function for point process on a Euclidean space to point processes on the product space and study the second order moment properties of point processes in the case of first and second order separability. Publication E develops an estimation procedure for the pair correlation function based on estimation equations that comes from variational equations. Paper F discusses the existence, moment properties, and estimation procedure of log-Gaussian Cox processes when the spatial locations are on the sphere.

Bedømmelsesudvalg/Assessment committee:

Professor Morten Nielsen, AAU
Associate professor Frédéric Lavancier, Université de Nantes
Associate professor Ethan Anderes, UC Davis Department of Statistics


Professor Morten Nielsen


Professor Jesper Møller, Aalborg Universitet, Professor Rasmus Waagepetersen, Aalborg Universitet og Emilio Porcu, School of Mathematics and Statistics & Chair of Spatial Analytics Methods, University of Newcastle




Institut for Matematiske Fag, Aalborg Universitet


Skjernvej 4A, rum 5.034

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02.05.2019 kl. 13.18

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