Outline.
Statistics 222 /
Geography M272 / Urban Planning M215:
Spatial Statistics, Prof. Rick Paik Schoenberg.
FALL 2007.
Lectures: Tues/Thur 12:30-1:45pm in Rolfe 3126
Texts:
1) Cressie, Noel A. C. Statistics for spatial data, revised
edition. Wiley, NY.
The text is on reserve in the SEL-EMS library.
2) Daley, D. and Vere-Jones, D. An Introduction to the Theory of Point
Processes, 2nd edition. Springer, NY.
3) There is also an optional supplementary text:
Ripley, Brian D. Spatial Statistics. Wiley, NY.
Office hours: Thursdays, 2:00 to 3:00 pm, MS 8965.
email: frederic@stat.ucla.edu
Statistics 222 will explore basic methods used in the analysis of
spatial data. Special attention will be paid to
spatial and spatial-temporal point processes.
The course will be both theoretical and
applied. Students will learn standard concepts in spatial data analysis,
and point process data analysis.
Examples from geography, epidemiology, environmental science,
neurology, and biology will be provided throughout the
instruction of the course, and students will implement the techniques
discussed in class using real data sets.
Dedicated students should come away with an in-depth understanding
of statistical concepts related to spatial statistics, as well as a thorough
comprehension of how and when
to implement various techniques in practice.
The course is designed for graduate students in any discipline
with solid mathematical
backgrounds and some knowledge of basic statistics.
A preliminary outline of the class is given below.
1. Simple Stochastic Models for Spatial Data
a. Basic definitions.
b. White noise.
c. Poisson processes.
2. Spatial autocorrelation and related concepts.
a. Definitions.
b. 2nd order and intrinsic stationarity.
c. Variograms.
d. Isotropic models and geometric anisotropy.
e. Ergodicity.
f. Relative variograms.
g. Spatial correlograms.
h. Nuggets and sills.
3. Estimation.
a. Separable covariograms.
b. Nonparametric covariogram estimates.
c. Variogram clouds, pocket plots, and median polishing.
d. Parametric covariogram estimation.
4. Spatial point processes.
a. Definitions.
b. Conditional rates and compensators.
c. Papangelou intensity.
d. Spatial point process models for clustering and inhibition.
e. Spatial-temporal models for clustering and inhibition.
f. Martingale techniques and residual analysis.
5. Smoothing and interpolation.
a. Moving averages.
b. Trend surfaces.
c. Contouring.
d. Prediction.
6. Tessellations.
a. Voronoi/Dirichlet tessellations.
b. Delaunay triangulation.
c. Other tessellations.