# Spatial Statistics

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ST 790M       Spatial Statistics

Description:
The course will cover the methodology and
modern developments for
spatial-temporal modeling estimation and prediction, Bayesian spatial
statistics and hierarchical frameworks, spatial point processes, data
assimilation and
spectral analysis of spatial processes. This course goes beyond standard
practices and exposes the students to
all the new developments and state of the art modern techniques for spatial
data.
All the methods presented will be introduced in the context
of a specific dataset, then the motivation behind a particular
method will be evident as it is developed.
Some of the lectures will be held
in the computer lab using the software R and WinBUGS, previous
knowledge of R will not required.

This course is meant to provide the students the necessary skills and knowledge
to
model and analyze data collected across space and time.
This course will complement ST733 (Applied Spatial Statistics).
While ST733 gives an organized and general introduction to spatial methods, in
the context of applications.
This new course goes beyond standard practices and exposes the students to
all the new developments and state of the art modern techniques, with an
emphasis in Bayesian practices and hierarchical frameworks, spectral methods and
space-time modeling, which is beyond the scope of ST733.

Web Site:
www.stat.ncsu.edu/people/fuentes/st790/

Instructor:
M. Fuentes

Schedule:
PATTERSON 208. 11:45-1:00PM

Credits: 3

Outline:

This course will cover a number of areas of spatial statistics and data assimilation applied to real,
scientific and interesting problems. A tentative list of more specific topics is as follows:

1. Introduction to spatial statistics:
a. Point level models
b. Areal (lattice) models
c. Spatial point processes.

2. Estimation and modeling of spatial correlations:
a. estimating variogram
b. fitting parametric models: Matern class
c. maximum likelihood estimation
d. restricted maximum likelihood

3. Prediction and Interpolation (kriging):
a. Lagrange multiplier approach
b. conditional inference approach
c. predicting at multiple sites
d. frequentist corrections for unknown covariance structure
e. model misspecification in kriging

4. Bayesian spatial statistics:
a. Bayesian estimation
b. Bayesian kriging
c. Bayesian priors for covariance parameters
d. Hierarchical Bayesian methods.

5. Spatial-temporal processes.
a. point-level modeling with continuous time
b. nonseparable models
c. dynamic space-time models
d. block-level modeling
e. misaligment problem.

6. Nonstationary spatial processes:
a. Bayesian deformation approaches
b. eigenfunction expansion of the covariance (EOFs)
c. kernel based methods
d. mixing of process distributions

7.Spatial Survival models:
a. parametric models (spatial frailty, logistic regression)
b. semiparametric models (beta mixture, counting process)
c. multivariate models

8. Spectral domain:
a. Fourier Theory
b. Spectral Representation of a Spatial Process
c. Spectral Density and periodogram
d. Spectral methods to approximate the likelihood
e. Increasing domain asymptotics
f. Infill asymptotics

9. Introduction to Data assimilation:
a. Kalman Filter
b. Extended Kalman filter
c. Ensemble Kalman filter
d. Particle Filter
e. A Bayesian framework for data assimilation

Some of the lectures will be conducted in the computer lab. Students will learn how to use existing
software, the emphasis of the course is to learn the methodology needed to do research on spatial
statistics and to analyze real data from the environmental, biomedical, geological and agricultural
sciences. The methods will be introduced with examples.

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