Spatio-temporal modeling and prediction

Course description

Modelling spatio-temporal phenomena is a key issue in today’s research. However, the extension from pure spatial to a spatio-temporal kriging approach is not trivial. We will look into a set of different perceptions of spatio-temporal dependence and the resulting covariance models (separable, product-sum, metric, …). The practical part deals with the exploration of empirical variograms and the different variogram models applied to different data sets. Finally, some computational aspects regarding R environment and specific packages available for variogram fitting and prediction purposes will be illustrated.

Structure (1 hour per step)

1. Step 1
   • Geostatistics and spatio-temporal random functions: theoretical framework on spatio-temporal random functions; properties of the spatio-temporal covariance function and semivariogram
   • Geostatistics and spatio-temporal random functions: an overview on some theoretical space–time covariances models
2. Step 2
   • Introduction to different formats of spatial and spatio-temporal in R: spatio-temporal full data frame; spatio- temporal sparse data frame; spatio-temporal irregular data frame
   • Reading and writing spatial and spatio-temporal data. Subset a spatio-temporal object. Graphical representation of spatio-temporal data
3. Step 3
   • Spatio-temporal structural analysis: semivariogram and covariogram estimation and model fitting
   • Semivariogram estimation. Fitting a spatio-temporal variogram model in R
4. Step 4
   • Spatio-temporal structural analysis: validation and comparison of spatio-temporal semivariogram and covariogram models; some statistical tests on semivariogram and covariogram characteristics
5. Step 5
   • Spatio-temporal prediction: spatio-temporal kriging; spatio-temporal kriging equations
   • Scripts in R to test some features of spatio-temporal covariance functions
6. Step 6
   • Spatio-temporal interpolation in R
   • Case studies by using spatio-temporal datasets

Target audience
Statisticians interested in applications involving earth sciences

Knowledge assumed (prerequisites)
Introduction to statistics (mandatory).
Introduction to geostatistics (recommended)

Preparatory material

Books

• Journel, A.G. and Huijbreghts, Ch.J. 1984. Mining Geostatistics, Academic Press, London (First edition published in 1978), 600 p.
• Hristopulos D. T. 2021. Random Fields for Spatial Data Modeling. A Primer for Scientists and Engineers, Springer, 867 p.
• Montero JM, Fernández-Avilés G, Mateu J. 2015. Spatial and Spatio-Temporal Geostatistical Modeling and Kriging Wiley, United Kingdom
• Sherman M, 2011. Spatial Statistics and Spatio-Temporal Data. Covariance Functions and Directional Properties. Wiley, United Kingdom
• Cressie, N., Wikle, C., 2011. Statistics for Spatio-Temporal Data. Wiley, New Jersey, 588 p
• Christakos, G., 2012. Modern Spatiotemporal Geostatistics. Dover Publications, Reprint edition. New York, 288 p
• Christopher K. Wikle, Andrew Zammit-Mangion, and Noel Cressie, 2019. Spatio-Temporal Statistics with R. Chapman & Hall/CRC

Papers

• Pebesma EJ 2020. CRAN Task View: Handling and Analyzing Spatio-Temporal Data. Version 2020-03-18, URL https://CRAN.R-project.org/view­SpatioTemporal.
• Pebesma EJ, Bivand RS 2005. “Classes and Methods for Spatial Data in R.” R News, 5, 9–13. URL https://CRAN.R-project.org/doc/Rnews/.
• Pebesma EJ, Bivand RS, Ribeiro PJ 2015. “Software for Spatial Statistics.” Journal of Statistical Software, 63(1). doi:10.18637/jss.v063.i01.