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, 2-3pm, MS 8965.
Email: frederic@stat.ucla.edu
Course Website: http://www.stat.ucla.edu/~frederic/222/F07
Outline.
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.
Grading:
Midterm exam (40%),
Written project (50%),
Oral presentation/participation (10%).
No homework except for the data analysis project.
Attendance in class is generally not mandatory and not counted as
part of the grade. However, the last week of class is an exception:
all students MUST attend class, on time, for the final week.
There will be no extensions for the project or presentation and no make-up
for the exam.
Students who are unable to make these dates or otherwise
fulfill the course requirements
must consult with the instructor in advance, if possible.
Students with learning disabilities must consult with the instructor
by the 2nd week of class
if special arrangements are required.
Midterm exam: Thursday, Nov 8, in class.
Written Project: due Friday, Dec 6, in class.
Oral presentation: Last week of class.
Description of Written Project: Find a spatial dataset and analyze it
using some of the relevant methods
described in class. Your report should contain 3-5 pages
of written text, followed by as many figures as appropriate. You may include as
many figures as you like, but all figures must appear AFTER the text, not
in the text, and the text part of the report must not exceed 5 pages,
double-spaced. Do not submit any computer code with your report.
In selecting your dataset
choose something that interests you, and try to have a main, answerable question
in mind.
Begin your paper with an introduction, a description of your data and how
they were obtained, and a summary of the main question(s) to be addressed
in your paper. Then summarize your analyses, paying very special attention
to any assumptions you are making and the plausibility of those assumptions.
Conclude by assessing how effective the methods you used were in helping
to answer your main question or questions.
You may use any software of your choice
for your analysis, but we will only discuss implementation in R in the course.
Oral presentations of project results will take place on the last week of
class. These will involve simply presenting a clear and
concise 5-minute summary of the main results from your analysis.