Spatial Statistics 2016

Email : jdrs@aya.yale.edu (the best way to reach me)

Phone : (860) 906-8197 (cell / text)

Office Location : 205 Prospect Street, Room 3c (first floor)

Drop in in CSSSI : Tuesdays and Thursdays, 2:30-4pm

Office Hours – You are STRONGLY encouraged to come and talk to me about class questions and about general statistics questions. Please sign up for a time to meet with me - click here- that way you won't be waiting around needlessly.

Mondays : 11am-noon, 1:15-3:15

Tuesdays : 12-12:30pm

Thursdays : 12-12:30pm

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Email :

Office Hours -

The Prerequisites :

An Introductory Statistics Course such as FES 714a or STAT 101-106 (various forms of introduction to statistics), and at least one other more advanced statistics course (such as a regression course). Understanding of symbolic notation is presumed. If you know GIS or R, all the better, but not required. Linear Algebra also helpful but not required.

The Goals :

An introduction to spatial statistics as applied primarily to the ecological sciences, but with applications and examples in several fields. The emphasis is on practical application to data of interest to YOU. Classes will consist of lectures and detailed examples. Extensive computer work is required in the homework.

The Books and Software

There are two main topics we'll cover : point processes and geostatistics. There isn't a single book that covers both these topics well, so we'll use several sources. For geostatistics, we'll primarly use Diggle and Ribeiro's Model Based Geostatistics which is a FREE Yale electronic resource. The images to the right provide links to Amazon.com for purchasing hardcopy titles (or electronic versions).

Diggle and Ribeiro : Model-based Geostatistics (Springer 2007). FREE Yale Electronic Resource. Understandable, good examples, BUT doesn't cover point processes - so great for the first half of the course. Noted below as MBG.
Waller and Gotway : Applied Spatial Statistics for Public Health Data. A good read, very thorough, and very comprehensible. Nice examples and web links. It's a public health book, but the examples are applicable to Environmental applications. Noted below as WG. You can get this book in it's electronic format for FREE - click here (then choose online book : must be from a Yale computer). Good for point processes.
Diggle : Statistical Analysis of Spatial and Spatio-Temporal Point Patterns, Third Edition. You can get this book in electronic format for FREE - click here (choose online book, must be on Yale computer). Excellent book. Noted below as . DIG.
Bailey and Gatrell : Interactive Spatial Data Analysis. This is the easiest to read of the books listed here, and a nice introduction to most of the topics. The disk in the back is basically useless, but these datasets are available here in a single file and in the resources folder at the left in separate named files (thanks to Tim). Noted below as BG.
Baddeley, Rubak, Turner : Spatial Point Patterns : Methodology and Application with R. This is an AWESOME book. I'm going to put a truncated version of similar notes online. Discuses how to use spatstat package with lots of examples. Clear writing but with all the details. Alas, not free.$100 hardback, $70 ebook. Noted below as BRT.
Mitchell : ESRI Guide to GIS, Volume 2 - Spatial Measurents and Statistics. An excellent intro to the Spatial Analyst in GIS. Good for point processes, and global measures of association (Morna's I, Geary's C). Very readable and cheap if used on Amazon (2005, no more recent version).
ArcGIS 9 : Using ArcGIS Geostatistical Analyst : An excellent intro to the Geostatistical Analyst in GIS. Good for Kriging, Co-kriging, etc. Very readable and cheap if used on Amazon (2004, no more recent version). ALSO : see ESRI tutorial for Geostatistical Analyst in ArcGIS 10 (PDF File Online Link). ALSO video intro to Kriging in GIS
Isaaks and Srivastava : Applied Geostatistics. A good book, but somewhat more difficult to follow, examples are not as easily reproduced. Still, very applicable. Noted below as AG.
Cressie : Statistics for Spatial Data. The Bible on Spatial Statistics, with all the math, not for the faint of heart. Probably a good read after you've taken this course. Noted as Cressie.
Legendre and Legendre. Numerical Ecology, Elsevier 1998. The Bible of Multivariate Stats for Ecology, but chapter 13 is all Spatial Stats. A good intro to spatial topics. It's dense and there is lots of math, but it's well written. If you get serious about statistics and ecology, eventually, you'll own this book. Noted below as NE.

Software : We will primarily use the R statistical software package this semester. We will also make some use of ArcGIS. ArcGIS is available on many computers around campus (FES computer labs, GIS lab, STATLAB, etc) and R is available on the web for FREE so you can download and use on your own computer (click here to get R).

Tim and Co. have set up an R-help website : http://environment.yale.edu/biometrics/yaleRWeb

The STATLAB website is an excellent source of information about several of these packages (click here).

The Requirements

Readings : Suggested for each class.

DATASETS

During the first two weeks of class, you need to find a spatial dataset that you will use for the semester.

This can be any dataset you like - BUT it must meet the following criteria -

Must have at least 20 observations and at least 3 variables
At least two of the variables must be continuous
Must be appropriate to spatial analysis (we help determine this part)

You can (and are encouraged) to work in groups of 2-3 people on a single dataset

Feel free to talk to Tim and Jonathan about any questions you have about the appropriateness of your dataset.

During the semester, we'll ask you to regularly apply methods we discuss to your data as appropriate. Once or twice you'll be asked to present spatial statistical results on your dataset in class. We'll have 'loaner' datasets you can use if a particular topic isn't appropriate for your data.

Project : At the end of the semester, you/your group will analyze your dataset using spatial techniques as appropriate. This will be graded according to a standard percentage system. We expect that you and/or your group will meet with us to discuss your project!!

The Grades :

Grades will be based on class presentations, the final project, class participation, and work on your dataset throughout the semester. Bascially, you'll get out of this class what you put into it.

The Examples

We will use a wide range of examples from forestry, biology, ecology, public health, etc. You are encouraged to bring interesting datasets to our attention.

The Lectures

Lecture notes will all be available on the classesv2 server either before or immediately after class.

The Schedule

Topics may be added or subtracted depending on class interest. The schedule is certain to change.

MBG : Diggle and Ribeiro : Model Based Geostatistics

BG : Bailey and Gatrell : Interactive Spatial Data Analysis.

WG : Waller and Gotway : Applied Spatial Statistics for Public Health Data.

AG : Isaaks and Srivastava : Applied Geostatistics.

Cressie : Cressie : Statistics for Spatial Data

NE : Legendre and Legendre. Numerical Ecology

Week	Dates	Monday	Reading
1	17, 19 January	Introduction Review of Linear Algebra/Matrices
2	24, 26 January	Spatial point patterns	Waller & Gotway, section 7.4
3	31, 2 February	Spatial point patterns	Waller & Gotway, section 7.5
4	7, 9 February	Spatial point patterns
5	14, 16 February	Global indices of spatial autocorrelation: Moran’s I and Geary’s c
6	21, 23 February	Geostatistical modeling with MBG book
7	28 Feb, 2 March	Geostatistical modeling with MBG book
8	7, 9 March	Geostatistical modeling with MBG book
	Spring break
9	28, 30 March	Variograms & kriging
10	4, 6 April	Variograms & kriging
11	11, 13 April	Co-kriging
12	18, 20 April	Geographically Weighted Regression
13	25, 27 April	PRESENTATIONS

The Software Examples

R CODE EXAMPLES
Example of Spatial Poisson PP
Simulated Poisson PP
Spatial PP Quadrat Counts
Kernel Smoothing for PPP
K and L Functions
G and F and J Functions
Clark Evans and Chi-Square Test of CSR
Kernel Ratio Intensity Estimates
Marked PPP
Heterogenous Poisson PP Models and Functions
Global Indices of Spatial Autocorrelation

(Rev. 2.6.17)

Week

The Software Examples