Spatial Statistics (FS 2018)

Lecturer

  • Prof. Dr. David Ginsbourger

Date and Venue

  • Monday, 13 - 15 h, B1 (ExWi)
  • Friday, 08 - 10 h, B78 (ExWi)
  • Start: Monday, February 19, 2018

Details

  • 6 ECTS credit points
  • Administrative information (Gefässe/blocks, registration for exam): KSL
  • Further information (contents, exercise series etc.): ILIAS

Contents

In this course we will focus on stochastic approaches for modelling phenomena taking place in multivariate spaces. Our main focus will be on random field models and on statistical methods for model-based spatial statistics. Starting from generalities on random fields, we will subsequently cover topics in spatial interpolation, analysis and simulation of random field paths, model selection and parameter inference, as well as experimental design. Potential additional topics include point pattern analysis and multiple-point statistics simulation. A tentative schedule follows:

  • Introduction to random fields
    • Definition, construction and examples
    • Notions of stationarity, continuity/differentiability, etc.
    • Variography and related topics
  • Spatial prediction
    • Best Linear Unbiased Prediction / Simple Kriging
    • The Gaussian case: interpretation and (conditional) simulation
    • Parameter estimation and extensions of Kriging
  • On path properties and decompositions of random fields
    • General results on path continuity/differentiability
    • Reproducing Kernel Hilbert Spaces ane the Loève isometry
    • Advanced results on Gaussian random fields
  • Topics in experimental design
    • Static and sequential model-based design with fixed or plugged-in covariance parameters
    • Experimental design accounting for parameter estimation
    • Towards optimization and set estimation strategies