Spatial and spatio-temporal statistics



Peter Guttorp (guttorp at uw dot edu)
Paul D. Sampson (pds at stat dot washington dot edu)

Faculty Contacts

SFU: Liangliang Wang (liangliang_wang at
UBC-V: Jim Zidek (jvzidek at
UBC-O: John Braun (john.braun at


TuTh 2:30-4
Sep 28-Nov 30 (no class Nov 23)


UW: Padelford C 301
SFU: WMC 2522
         SSCK 9509 (Th 10/12 ONLY)
UBC-V: ESB 4192
UBC-O: ASC 304 (Tu)
               SCI 331 (Th)  

Office hours

In person or by Skype:

Peter Guttorp Tu 12-1 (Padelford B-318, skype name guttorp)
Paul Sampson Th 11-12 (Padelford B-319, skype name stossdad)


Knowledge of regression and some understanding of likelihood at MSc level. Familiarity with R (most likely you will want to have R on your laptop).

Course content

1. Kriging (9/28)

Spatial estimation at unobserved sites. Some history. The Gaussian regression theory. Simple and ordinary kriging. Standard errors. Universal kriging. Bayesian kriging.
Slides (PDF).

2. Spatial covariance (10/3)

The key concept needed for spatial estimation. Classes of spatial covariance functions.
Slides (PDF).

You can download R here. The following libraries need to be installed: geoR, MASS, sp, splancs, RandomFields (but that can be done in class). You will also want to have X11 installed: here are possible sources for Windows, Mac, Linux.

Practicum 1: geoR (10/5)

Solution and comments (in red)

3. Nonstationary structures I: deformations (10/10)

Geometric anisotropy. Generalization to nonstationary models. Thin-plate splines. Principal warps.
Slides (PDF).

Practicum 2: Deformation model (10/12)

4. Nonstationary structures II: linear combinations etc. (10/17)

 Process convolution. Basis function approaches.
Slides (PDF).

Practicum 3:  Process convolution (10/19)

Paper by Risser and Calder.

5. Space-time models (10/24)

 Singular value decomposition. Space-time covariance. Dynamic linear models.

Practicum 4: SpatioTemporal (10/26)

6. Markov random fields (10/31)

Sparse precision matrices. Gaussian MRF simulation and estimation. The stochastic PDE approach. Integrated nested Laplace approximations.

Practicum 5: R-INLA  (11/2)

7. Misalignment and use of deterministic models (11/7)

Hierarchical models. Downscaling. Upscaling. Change of support.

Practicum 6: Chesapeake Bay (11/9)

8. Monitoring network design (11/14)

(Re)design of monitoring networks. The entropy approach.

9. Extremes (11/16)

Generalized extreme value distribution. Generalized Pareto distribution. Max-stable processes. Composite likelihood.

Practicum 7: SpatialExtremes (11/21)

10. Statistical climatology (11/28)

Space-time trends in regional climate models: means and extremes.

Practicum 8: Uncertainty in rankings (11/30)


For satisfactory work each student needs to solve eight of the homework problems (Last updated October 17)

With permission from the instructors, three problems can be substituted by a data analysis project. Solutions are to be sent electronically to Peter Guttorp. The first batch (of at least three problems) is due October 27, while the rest are due by December 1.

In addition, students need to answer the two practicum questions in at least four practica (you may work in groups of up to three). These reports should be sent to Paul Sampson, no later than December 3.


General books

Sudipto Banerjee, Bradley P. Carlin and Alan E. Gelfand (2014): Hierarchical Modeling and Analysis for Spatial Data, Second Edition. Chapman & Hall/CRC Press.

Stuart Cole (2001): An Introduction to Statistical Modelling of Extreme Values. Springer.

Noel Cressie and Christopher K. Wikle (2011): Statistics for Spatio-Temporal Data. Wiley.

Peter J. Diggle and Paulo Justiniano Ribeiro (2010): Model-based Geostatistics. Springer.

Alan E. Gelfand, Peter J. Diggle, Montserrat Fuentes and Peter Guttorp, eds. (2010): Handbook of Spatial Statistics. Section 2, Continuous Spatial Variation. Chapman & Hall/CRC Press.

Nhu D.Le, and James V. Zidek (2006): Statistical Analysis of Environmental Space-Time Processes. Springer.

Bertil Matérn (1986): Spatial Variation. Springer Lecture Notes in Statistics vol. 36. Reprint of his 1960 dissertation.

Influential papers

W. Meiring, P. Guttorp and P. D. Sampson (1998): Space-time estimation of grid-cell hourly ozone levels for assessment of a deterministic model. Environmental and Ecological Statistics 5: 197–222.

D. Damian, P. D. Sampson and P. Guttorp (2000): Bayesian estimation of semi-parametric non-stationary spatial covariance structure. Environmetrics 12: 161–176.

D. Higdon (1998): A process-convolution approach to modelling temperatures in the North Atlantic Ocean. Environmental and Ecological Statistics 5: 173–190.

Lindgren, F., Rue, H. and Lindström, J. (2011): An explicit link between Gaussian fields and Gaussian Markov random fields: the stochastic partial differential equation approach. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 73: 423–498.

W. F. Caselton and J. V. Zidek (1984): Optimal monitoring network designs. Statistics and Probability Letters 2: 223–227.