Lecture notes (ST 810 M)

Lecture notes will be updated and available on the day of the class.
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The notes are from a joint effort by Dr. Richard SMITH and Dr. Fuentes, the notes will be part of a book. You should complement the notes with readings for the 3 recommended books (available in the reserve room at the main library).

References in the notes
• Lecture 1 (pdf file).Lecture 1 (postscript file).
  Syllabus (pdf)Syllabus (ps).Outline (ps)Outline (pdf)
  Introduction to Spatial Statistics
  (pdf file) (ps file)
  An Example. The need for Spatial Statistics
  (08/22/2000)
  
• Lecture 2 (pdf file) Lecture 2 (ps file)
  Spatial processes, stationarity, and isotropy.
  (08/24/2000)
  
• Lecture 3 (pdf file) Lecture 3 (ps file)
  Examples of spatial processes, analysis of lack of stationarity and anisotropy for air pollution data: ozone,SO2, and nitric acid.
  8/29/00
  
• Lecture 4 (pdf file) Lecture 4 (ps file) Fitting algorithms for the semivariogram, and examples.
  8/31/00
  
• Lecture 5 (pdf file) Lecture 5 (ps file)
  Maximum likelihood estimate of the variogram parameters and examples.
  9/5/00
• LAB
  We meet in the SICL computer lab (Harrelson building #G100).
  I will show you how to estimate the parameters of the variogram (using Matern models, exponential...) with a Weighted Non-linear least squares approach, Maximum likelihood, and REML. I will use S+ and Fortran codes.
  9/7/00
  
• Lecture 6 (pdf file) Lecture 6 (ps file)
  Restricted Maximum likelihood estimate of the variogram parameters and examples.
  PAPER DISCUSSION TODAY Today we discuss one of most popular algorithms to model and predict NONSTATIONARY processes!! please read the paper assigned for today.
  9/12/00
  
• Lecture 7 (pdf file) Lecture 7 (ps file)
  Restricted Maximum likelihood and Bayesian estimate of the variogram parameters and examples.
  Wolfcamp aquifer data This is a data set from Cressie's book (chapter 4) and it is in pag. 74 of your notes. Please use this data set to practice and do the examples you have in your notes in pag. 72. (The first colon is x, second y, (x,y represent location in miles) and third the response, the fourth column has zeros (you need a column of zeros if you do not have replications just to use the fortran code for REML presented in the LAB 1).
  9/14/00
  
• Lecture 8 (pdf file) Lecture 8 (ps file)
  MINQE estimator of covariance parameters, and examples using the previous techniques learned: the Bayesian and likelihood estimates.
  PAPER DISCUSSION TODAY Today we discuss the ROBUST semivariogram proposed by Cressie!! please read the paper assigned for today.
  Davis topographical heights dataset This is a data set that will be discussed in class, you can use this dataset for your project! x (first column), y (second column) in feet, unit=50 feet, the third column is the heigh of the earth's surface withtin a 310 foot square. The fourth column is just zeros (you need a column of zeros if you do not have replications just to use the fortran code for REML presented in the LAB 1).
  useful Splus commands for WNLS and REML
  9/19/00
  
• Lecture 9 (pdf file) Lecture 9 (ps file) Examples of estimation of spatial correlation and kriging.
  9/21/00
  
• Lecture 10 (pdf file) Lecture 10 (ps file)
  how to efficiently compute the kriging predictor, with a conjugate gradient algorithm.
  Conditional Inference approach (pdf file (pdf file) (ps file )
  PAPER DISCUSSION TODAY Today we discuss one of most popular algorithms to fit a parametric model to the empirical semivariogram (the WNLS approach by Cressie)!! please read the paper assigned for today.
  9/26/00
  
• LAB
  We meet in the SICL computer lab (Harrelson building #G100).
  I will show you some tools for exploratory analysis, WNLS, ML, REML in Splus. And also, Bayesian analysis in Splus.
  DEADLINE TO SUBMIT THE ABSTRACT FOR YOUR PROJECT!!
  9/28/00
  
• Download 3 handouts: 1. Amendment to Lecture 10(pdf). ps file . Universal kriging predictor derived from a contidional probability.
  2. Lecture 11 (pdf). Lecture 11 (ps) Bayesian approach for prediction.
  Examples will be presented in class (using the S+ function krige.bayes, that I have updated).
  3. how to simulate the posterior (pdf) ps file
  10/3/00
  
• Lecture 12 (pdf) Lecture 12 (ps) Examples of the Bayesian approach to spatial prediction (handout given in class).
  Prediction at multiple sites, block prediction versus point prediction.
  Corrections for unknown covariance parameters (frequentist approach).
  10/5/00
  
• Lecture 13 (pdf) Lecture 13 (ps) Sensitivity of kriging to covariance misspecification (frequentist analysis).
  PAPER DISCUSSION TODAY Today we discuss a paper about approaches for nonstationary processes please read the paper assigned for today.
  10/10/00.
  
• Lecture 14 (pdf) Lecture 14 (ps)
  Median Polish and examples of kriging.
  10/12/00
  
• Lecture given by Marc Genton
  10/19/00
  

  References for Spectral domain
  

• Lecture 15 (pdf) Lecture 15 (ps) SPECTRAL DOMAIN: Fourier Analysis.
  PAPER DISCUSSION TODAY Today we discuss a paper about Space-Time Stochastic Model of Rainfall please read the paper assigned for today.
  10/24/00
  
• LAB TODAY
  10/26/00
  
• Lecture 16 (pdf) Lecture 16 (ps) SPECTRAL DOMAIN:Spectral representation of a process.
  10/31/00
  
• Lecture 17 (pdf) Lecture 17 (ps) SPECTRAL DOMAIN:Spectral densities.
  11/2/00
  
• Lecture 18 (pdf) Lecture 18 (ps) SPECTRAL DOMAIN:Estimating the spectral density, periodogram and other spectral tools.
  11/7/00
  
• Lecture 19 (pdf) Lecture 19 (ps) Tapering. ASYMPTOTICS
  11/9/00
  
• Lecture 20 (pdf) Lecture 20 (ps) Nonstationary spatial-temporal processes I.
  Summary of Bayesian approach for nonstationarity
  References for Chapter 3
  11/14/00
  
• Lecture 21 (pdf) Lecture 21 (ps) Nonstationary spatial-temporal processes II.
  11/16/00
  
  
• Lecture 22 (pdf) Lecture 22 (ps) LATTICE MODELS I.
  11/21/00
  
  
• Lecture 23 (pdf) Lecture 23 (ps)
  Appendix (pdf) Appendix (ps) LATTICE MODELS II and permutation tests for lattice spatial data.
  11/28/00
  
  
• Lecture 24 (pdf) Lecture 24 (ps) Introduction to Network design and examples.
  Example: "Quality data networks that minimize entropy" by Caselton, Kan and Zidek, Statistics in the environmental and earth sciences (1992)
  11/30/00
  

• Students presentations on 12/5/00.
  

• Dave Holland (EPA) and Jerry Davis (MEAS) will present some interesting applications of the spatial statistics tools learned this semester; EOFs, network design, spatial interpolation.
  12/7/00.

• Final due on December 11 at 11am.

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  It would be a good practice to attend all the lectures.

  Please send your feedback to fuentes@stat.ncsu.edu via e-mail.

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Last updated July 18, 2000.

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