MATH 432/532
Spring, 2016
Spatial Statistics
Professor: Amanda S. Hering
• Contact Information:
Office: Chauvenet 235
Phone: 303.384.2462
Email: ahering@mines.edu
• Office Hours: Tues/Thurs: 3:30 – 4:30 pm. Wed: 1 – 3 pm
Otherwise, by appointment only.
• Class Day/Time: 11:00 am – 12:15 pm TR
Class Location: Alderson 141
• Web Page link: http://inside.mines.edu/~ahering/math432_2016/spatial
The username and password will be given in class.
Instructional Activity:
3 Hours Lecture
0 Hours Lab
3 Semester Hours
Course Description:
Spatial statistics is a branch of statistics used to analyze data observed on a 2 or 3-dimensional surface with
either regular or irregular spacing. This type of data arises in almost every field of study, and much of the
early development of spatial data was driven by the needs of scientists in geography, mining, meteorology, and
geology. For example, petroleum companies collect wave strength information around off-shore oil platforms;
when mining for natural resources, drill hole data covering the spatial area of interest is collected; construction
companies compile information on soil type and compaction; geophysicists collect electromagnetic data to
recreate images of subsurface features; criminologists collect data on the location and characteristics of
crimes; traffic officers record the location and causes of vehicle collisions.
Spatial data must be handled carefully. As an example in geostatistics, observations in close spatial proximity tend to be more similar than would be expected if the observations are independent of each other.
This correlation must be handled carefully since ignoring the correlation among observations can cause an
investigator to seriously misrepresent (and frequently overstate) the confidence he or she has in applying
conclusions drawn from a sample to an entire population. This course will give senior-level and graduate
students the tools to analyze such data.
Many academic disciplines use software designed to meet their specific needs, but in this course, students
will learn how to use a free programming language (called R, which is closely related to S-PLUS) to develop
the tools needed to properly analyze spatial data. Learning to program in R gives students the power to
double-check their discipline-specific software, and it also gives them the flexibility to analyze data with
methods that are not automatically provided by their software.
Course Outline: The following is a rough list of topics that will be covered in this course:
• Geostatistical Data: Random fields; Variograms; Covariances; Stationarity; Nonstationarity; Kriging;
Simulations; Bayesian hierarchical models
• Lattice Data: Spatial regression; SAR, CAR, & MA models; Geary/Moran indices
• Point Patterns: Point processes; K-function; complete spatial randomness; Homogeneous/inhomogeneous
processes; Marked point processes
• Special Topics: Spatio-temporal modeling (if time permits)
Course Prerequisites: You are assumed to
1. have had an introductory statistics course, covering content such as confidence intervals, hypothesis
tests, random variables, p-values, etc. (such as MATH 201, 335, or 530);
2. know linear regression (such as MATH 424 or 531); and
3. know the multivariate normal distribution and its properties (from MATH 334 and/or MATH 437).
Required Textbook: Waller, L. and Gotway, C. A. (2004) Applied Spatial Statistics for Public Health
Data. Wiley.
(Optional) Bivand, R. S., Pebesma, E. J., and Gómez-Rubio, V. (2008) Applied Spatial Data Analysis with
R. Springer Science + Business Media; ISBN: 978-0-387-78171-6
Can be accessed for free through the university at the following website:
http://www.springerlink.com/content/978-0-387-78170-9/#section=147789&page=13&locus=57
Other References: This is a list of other commonly used texts in spatial and space-time statistics.
Banerjee, S., Carlin, B. P., and Gelfand, A. (2003) Hierarchical Modeling and Analysis for Spatial Data.
Chapman & Hall/CRC.
Cressie, N. (1993) Statistics for Spatial Data. Wiley.
Cressie, N. and Wikle, C. (2011) Statistics for Spatio-Temporal Data. Wiley.
Diggle, P. J. (2003) Statistical Analysis of Spatial Point Patterns. Hodder Arnold.
Diggle, P. J. and Ribeiro, R. J. (2007) Model-based Geostatistics. Springer*.
Haining, R. (1990) Spatial data analysis in the social and environmental sciences. Cambridge.
Le, N. D. and Zidek, J. V. (2006) Statistical Analysis of Environmental Space-Time Processes. Springer*.
Møller, J. and Waagepetersen, R. P. (2003) Statistical Inference and Simulation for Spatial Point Processes.
Chapman & Hall/CRC.
Schabenberger, O. and Gotway, C. A. (2005) Statistical Methods for Spatial Data Analysis. Chapman &
Hall/CRC Press.
Stein, M. L. (1999) Interpolation of Spatial Data. Some Theory for Kriging. Springer.
Wackernagel, H. (2003) Multivariate Geostatistics: An Introduction with Applications. Springer.
*Denotes texts available through CSM’s library access to Springer via
http://www.springerlink.com.
Student Learning Outcomes:
Upon successful completion of Spatial Statistics, students will be able to:
1. Identify the three basic types of spatial data and know the approaches used in analyzing each type.
2. Apply the concepts of spatial statistics to real datasets.
3. Use the R software (or other software package of your choosing) to perform spatial analysis of real data
sets.
4. Communicate findings from a real spatial data analysis in both written and oral formats.
Grading Procedures:
Homework Assignments:
Late Term Exam:
Project:
Total:
30%
30%
40%
100%
90 - 100%
80 - 89%
70 - 79%
60 - 69%
Below 60%
A
B
C
D
F
Please be aware that nothing can be done to change a grade once it has been earned. There is no extra
credit or any change that can be made on an individual basis.
HOMEWORK:
Approximately weekly homework assignments will be given in each of the Weeks 1 through 12 of the semester.
Hard copies of assignments will be collected at the START of class on the due date. Late assignments will
not be accepted. The lowest homework grade will be dropped.
EXAM:
There will be one in-class closed book exam tentatively scheduled in Week 12, probably April 14th.
PROJECT:
A project will be due at the end of the semester, and a presentation of the work will be held in place of the
class’ 2-hour final exam. More details will be given as the semester progresses. Late projects will not be
accepted.
COURSEWORK RETURN POLICY:
Barring any unforeseen circumstances, coursework will be graded and returned to students within two weeks.
Feedback will be provided on all coursework, or solutions will be posted.
Notes: A few more things...
• Check the website frequently for updates.
• I would like to know about any particular academic difficulties or personal problems that are affecting
a student’s performance.
Absence Policy:
The website http://inside.mines.edu/Student-Absences outlines CSM’s policy regarding student absences. It contains information and documents to obtain excused absences. Note: “All absences that are not
documented as excused absences are considered unexcused absences. Faculty members may deny a student
the opportunity to make up some or all of the work missed due to unexcused absence(s). However, the
faculty members do have the discretion to grant a student permission to make up any missed academic work
for an unexcused absence. The faculty member may consider the student’s class performance, as well as
their attendance, in the decision.”
Disability Accommodations:
The website http://disabilities.mines.edu/accommodations.html outlines CSM’s disability services.
The AMS department requests that any student requiring accommodations contact the instructor via email
or individual meeting within the first two weeks of class or within two weeks of receiving the accommodation.
Policy on Academic Integrity/Misconduct:
The Colorado School of Mines affirms the principle that all individuals associated with the Mines academic
community have a responsibility for establishing, maintaining an fostering an understanding and appreciation
for academic integrity. In broad terms, this implies protecting the environment of mutual trust within which
scholarly exchange occurs, supporting the ability of the faculty to fairly and effectively evaluate every students
academic achievements, and giving credence to the universitys educational mission, its scholarly objectives
and the substance of the degrees it awards. The protection of academic integrity requires there to be clear
and consistent standards, as well as confrontation and sanctions when individuals violate those standards.
The Colorado School of Mines desires an environment free of any and all forms of academic misconduct and
expects students to act with integrity at all times.
Academic misconduct is the intentional act of fraud, in which an individual seeks to claim credit for the work
and efforts of another without authorization, or uses unauthorized materials or fabricated information in any
academic exercise. Student Academic Misconduct arises when a student violates the principle of academic
integrity. Such behavior erodes mutual trust, distorts the fair evaluation of academic achievements, violates
the ethical code of behavior upon which education and scholarship rest, and undermines the credibility of
the university. Because of the serious institutional and individual ramifications, student misconduct arising
from violations of academic integrity is not tolerated at Mines. If a student is found to have engaged in such
misconduct sanctions such as change of a grade, loss of institutional privileges, or academic suspension or
dismissal may be imposed.
The complete policy is online at http://bulletin.mines.edu/undergraduate/policiesandprocedures/.
Important Dates:
Jan 28th
Mar 14-18th
Apr 7
Apr 12 or 14th
May 5
May 7-12
Last day to register, add, or drop without a “W”
Spring Break (No Classes)
Last day to withdraw for continuing students
In Class Exam
Last day of classes
Final Exams
Tentative Course Outline:
Week
0
Dates
Jan. 14
Textbook
Chapter 1
Topic
Types of Spatial Data, Accounting for Dependence
1
Jan. 19/21
Chapter 4
Coordinate Systems, Visualization, Smoothing
2
Jan. 26/29
Section 8.1, 8.2
3
Feb. 2/4
Section 8.2
Semivariogram Models and Fitting
4
Feb. 9/11
Section 8.3
Simple, Ordinary, and Universal Kriging
5
Feb. 16/18
Lattice/Areal Data
Section 7.4, 7.5, 9.1 Global and Local Dependence
6
Feb. 23/25
Section 9.1, 9.2, 9.4
Spatial Regression Models
7
March 1/3
Section 9.2, 9.3
SAR and CAR Models
8
March 8/10
Spatial Point Patterns
Section 5.1, 5.3
CSR, HPP, K-functions
–
March 15/17
Spring Break
—
9
March 22/24
Section 5.2, 5.4
IPP, Intensity, Other Patterns
10
Mar 29/31
Paper
Multivariate Spatial Point Patterns, Residuals
11
April 5/7
Guest Lecture
12
April 12/14
NA
Review/Questions/In-Class Exam
13
April 19/21
NA
Sample Research Projects
Land Cover/Crime/Groundwater
14
April 26/28
Papers
Multivariate/Categorical Geostatistics
15
May 3/5
TBD
Space-Time Models
16
May 7-12
Final Exams
Geostatistics
Population and Empirical Semivariograms
Special Topics
TBD