SFU: STAT 890

UBC-V: STAT 547L

UBC-O: STAT 547O

Peter Guttorp (guttorp at uw dot edu)

Paul D. Sampson (pds at stat dot washington dot edu)

SFU: Liangliang Wang (liangliang_wang at sfu.ca)

UBC-V: Jim Zidek (jvzidek at gmail.com)

UBC-O: John Braun (john.braun at ubc.ca)

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)

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).

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

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.

Solution and comments (in red)

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

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

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

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

Hierarchical models. Downscaling. Upscaling. Change of support.Slides.

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

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

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

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.

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.

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.