FALL 2009.

Lectures: Tues/Thur 9:30-10:45am in Math-Science 5203

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: Mondays, 12 to 12:50 pm, MS 8965.

email: frederic@stat.ucla.edu

Course Website: http://www.stat.ucla.edu/~frederic/222/F09 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.

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 5, in class.

Written Project: due Thursday, Dec 3, in class.

Oral presentations: 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 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 week of class. These will involve simply presenting a clear, concise, and very brief summary of your data and one or two of the main results from your analysis.