Spatial Statistics

Statistical models for spatially varying phenomena, and statistical methods to learn about such phenomena based on data points with spatial coordinates. The most common example of "space" is a geographical area. More specifically, the course contains model specification, simulation, prediction, and parameter estimation, for continuously- and discretely-indexed random fields, and for point processes. Specifically for Gaussian, Poisson and Markov random fields. Examples from ecology, epidemiology and geophysics.

1.Knowledge: The student has knowledge about basic concepts of the theory about Gaussian random fields, including algorithms for unconditional and conditional simulation, and spatial prediction by various types of kriging. The student also has knowledge about basic concepts of the theory of point processes, spatial Poisson and Cox random fields, and MCMC-algorithms for simulation of such point processes. Moreover, the student has knowledge about basic concepts of the theory of Markov random fields, including concepts as cliques, neighborhoods and potential function and insight into the Hammersley-Clifford theorem. Further, knowledge of simulation of Markov random fields by use of MCMC algorithms. Lastly, the student has knowledge of the basic theory of parameter estimation in spatial random fields.

2. Skills: The student can formulate statistical models for simple spatial phenomena, and perform parameter estimation under these models by use of suitable computer software. Moreover, the student can evaluate conditional models by stochastic simulation and perform spatial prediction.

Lectures and compulsory work (projects).