University of Florida

ABE 6933
Spatial Statistics

Semester Taught - Fall

Catalog Description

Credits: 3

This course is an introduction to spatial statistics, with a focus on methods that are relevant for public health applications, as well as earth and environmental sciences. It is primarily intended for two audiences: (i) statisticians who want to get exposed to methods and applications and (ii) researchers from other elds with some training in statistics that routinely work with spatial data and would like to learn appropriate statistical models and methods. Many of the methods and models are applicable to analysis of general - not necessarily spatially - dependent data, and may appeal to students not immediately interested in spatial statistics per se.

Pre-requisites/Co-requisites

  • sufficient background: first-year required masters-level coursework in statistics at UF
  • minimal sufficient background: a solid graduate course in regression (such as STA6207) with exposure to matrix notation; a solid course in inference at the level of STA5328; basic scientific and statistical computing skills; motivation (particularly, to pick up R)
  • ideal background: in addition to the minimum background above, proficiency with matrix algebra and basic numerical linear algebra (STA6329); statistical computing using R; exposure to linear mixed models, generalized linear models and generalized linear mixed models; masters level sequence in probability and inference STA 6326-6327; interest (and/or need!) to apply methods learned in this course in your research work.

A homework assignment distributed during the first week of classes will give students a good idea of expected background and whether they should be taking this course for a letter grade. Interested students outside of stats/biostats with slightly less stats background than minimal sufficient (but with greater than average level of motivation and interest in select topics) are encouraged to contact the instructor to discuss "custom options".

Course Objectives

Objectives of the course are that students be able, by the end of the course, to

  • describe the three main areas of spatial statistics: methods for geostatistical, areal, and point process data;
  • read and discuss new methods in spatial statistics in the literature based on an understanding of the basic spatial statistics approaches, principles and main assumptions,
  • evaluate which methods to use for spatial datasets that may arise in their research; and
  • implement various methods using statistical software

Instructor

Dr. Nikolay Bliznyuk
Office: Room 239 Rogers Hall
Phone: 392-1864 x239

Material/Supply Fees

None.

Class Materials Required

Texbook:

No required texts as lecture notes and readings will be distributed via a Dropbox course folder. A number of recommended supplementary texts will be put on course reserve at Marston Science Library.

Reference Texts:

  • Schabenberger and Gotway (2004), Statistical Methods for Spatial Data Analysis.
    Quite readable; we'll cover a number of topics from the rst 6 chapters of this text.
  • Cressie (1993), Statistics for Spatial Data.
    Used to be the bible of spatial statistics. Somewhat outdated now but still extremely useful.
  • Cressie and Wikle (2011), Statistics for Spatio-Temporal Data.
    A nice modern complement to Cressie's bible.
  • Banerjee, Gelfand, Carlin (2003), Hierarchical Modeling and Analysis for Spatial Data.
    Good for a Bayesian viewpoint on spatial modeling and tting using Markov Chain Monte Carlo (using WinBugs). Has separate chapters on areal models and on more advanced topics. Many code examples. Second edition is out!
  • Wood (2006), Generalized Additive Models: An Introduction with R.
    A superb text for additive, generalized additive and generalized additive mixed models. A nice complement for the R package mgcv developped by Wood as it has many code examples.
  • . . . and a few other texts

Course Outline

Methods, models and some theory behind will be motivated by applications and supplemented with discussion of implementation of various spatial methods using statistical environment R (mgcv, spBayes, INLA) and, possibly, WinBugs (both freely available). The main goal is to disect methods and models in order to understand them, rather than to apply black-box procedures in existing software to carry out standardized
analysis of data.

Lectures will cover the three main areas of spatial statistics: geostatistical (point-referenced) data, lattice (areal) data, and point process data. Tentative list of topics (with possible reordering at the discretion of the instructor) is provided below:

  • (geostatistical) models for point-referenced data (overview)
  • some theory for point-referenced stochastic processes (e.g., temporal, spatial, general Gaussian)
  • areal data models (overview)
  • spatial point process models (overview)
  • variogram and covariance function estimation
  • spatial prediction and kriging
  • spatial regression: mixed models, semiparametric models, additive and generalized additive models
  • advanced topics: hierarchical models, spatial misalignment, non-stationary models, spatio-temporal processes, multivariate random _elds, INLA and SPDE models

Grading

Homework 40%
Project 40%
Final Exam 20%
Participation up to 10%

(Yes, the numbers do add up to 110%, and you can end up with a"AAA" as the course grade.)

Homework: There will be 5-6 homework assignments, with greater frequency in the first half of the course.Some assignments will be more analytical, others will deal with data analysis and implementation of procedures in R. Unless noted otherwise, (i) assignments must be completed by students individually, but group discussion is permitted; (ii) all work that you submit must be your own and you should be able to justify your work (failure to do so typically makes instructors very upset). Additional guidelines (particularly, regarding submission and deadlines) will be provided along with each assignment.

Project: choose one of the following options (or propose an alternative to the instructor)
1. Data analysis option: perform a statistical data analysis illustrating the application of methods discussed in class, or related spatial statistics methods, to real data. Ideally, the data will come from your own line of work.
2. Methods option: study a method or methods of spatial statistics from modern literature not presented in class, implement and/or study/illustrate the method on real or simulated data.
3. Theory option: study and briefly summarize a paper on material not covered in class, critically review and relate to other literature.

In addition to carrying out the project work, a student will need to
1. submit a project proposal (1-2 pages long; must outline your goals and a proposed strategy of accomplishing them), which must be approved by the instructor
2. write a short report in the form of a scienti c paper (i.e., containing abstract, introduction, methods, results succinctly summarized using text, tables and gures, discussion, references and supplements including code) summarizing the project; length - 8-10 double-spaced pages (not counting supplements)
3. potentially, present your work in class (tentatively, during the last 2 weeks of classes)

Depending on the size of the class, work in small groups may be permitted. It is not unreasonable to expect that students working in a group will attempt a more ambitious project than soloists (hint, hint!). You will be assessed on the clarity and correctness of your presentation and quality of your report. Other details will be released after the rst week of classes.

Final exam: details will be announced during the rst few weeks of classes; potentially, it could be a longer-than-typical-homework take-home assignment.

Participation: I do not want to curb students' creativity in interpreting \participation"; some of the proven ways to participate include being alert and getting involved in class (for which attendance is necessary but not sufficient), making use of the course forum to discuss course material and organizational matters, providing anonymized or open feedback about the course, etc. Participation in these activities will allow the instructor to make a more objective assessment of your participation.

Academic Honesty

As a student at the University of Florida, you have committed yourself to uphold the Honor Code, which includes the following pledge: “We, the members of the University of Florida community, pledge to hold ourselves and our peers to the highest standards of honesty and integrity.”  You are expected to exhibit behavior consistent with this commitment to the UF academic community, and on all work submitted for credit at the University of Florida, the following pledge is either required or implied: "On my honor, I have neither given nor received unauthorized aid in doing this assignment." 
 
It is assumed that you will complete all work independently in each course unless the instructor provides explicit permission for you to collaborate on course tasks (e.g. assignments, papers, quizzes, exams). Furthermore, as part of your obligation to uphold the Honor Code, you should report any condition that facilitates academic misconduct to appropriate personnel. It is your individual responsibility to know and comply with all university policies and procedures regarding academic integrity and the Student Honor Code.  Violations of the Honor Code at the University of Florida will not be tolerated. Violations will be reported to the Dean of Students Office for consideration of disciplinary action. For more information regarding the Student Honor Code, please see: http://www.dso.ufl.edu/sccr/process/student-conduct-honor-code.  

UF Counseling Services

Resources are available on-campus for students having personal problems or lacking clear career and academic goals which interfere with their academic performance. These resources include:

  1. University Counseling Center, 301 Peabody Hall, 392-1575, personal and career counseling;
  2. Student Mental Health, Student Health Care Center, 392-1171, personal counseling;
  3. Center for Sexual Assault/Abuse Recovery and Education (CARE), Student Health Care Center, 392-1161, sexual assault counseling;
  4. Career Resource Center, Reitz Union, 392-1601, career development assistance and counseling.