Outline.
Statistics 222 /
Geography M272 / Urban Planning M215:
Spatial Statistics, Prof. Rick Paik Schoenberg.
FALL 2011.
Lectures: Tues/Thur 2pm-3:20pm in Boelter 5264.
Texts:
1) Cressie, Noel A. C. Statistics for spatial data, revised
edition. Wiley, NY.
The text is on reserve in the SEL-EMS library.
There are also 2 optional supplementary texts:
2) Daley, D. and Vere-Jones, D. An Introduction to the Theory of Point
Processes, 2nd edition. Springer, NY.
3) Ripley, Brian D. Spatial Statistics. Wiley, NY.
Office hours: Thursdays, 12:30pm to 1:30 pm, MS 8965.
email: frederic@stat.ucla.edu
Course Website: http://www.stat.ucla.edu/~frederic/222/F11
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, 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.
Grading:
Midterm exam (40%), Written project (55%),
Oral presentation/participation (5%).
Attendance in class is generally not mandatory and not
counted as part of the grade.
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 3, in class.
Written Project: due by email in pdf to
frederic@stat.ucla.edu by Thur, Dec 8, 11:59pm.
Oral presentations: Nov 29-Dec 1.
No class Thur, Nov 24 (Thanksgiving).
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 questions 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 2 class periods.
These will involve simply presenting a clear, concise, and very brief summary of
your data and a couple of the
main results from your analysis.