STA293: Simulation Based Spatial Statistics
||Mon - Fri 9:00am-5:00pm
||Mon & Wed 2:00-3:00pm
||025 Old Chem
||Brian D. Ripley,
||Statistical Inference for Spatial Processes
||Statistics for Spatial Data|
|Brian D. Ripley,
|Brian D. Ripley,
||The Demon-Haunted World|
(Science as a Candle in the Dark)
This course is designed for students and researchers with spatial data,
or other dependent data. Emphasis will be on Markov random field models
like those useful in hydrology and many other areas of spatial statistics.
A mix of well-known methods and recent developments will be presented.
We will cover two related topics:
- Building models for spatial (or otherwise dependent) processes
- Simulation of and inference from these processes.
Prerequisites for the course are:
- proficiency in some computing language
(for example: C, FORTRAN, Splus, Matlab, Mathematica)
- some proficiency in statistics. We will assume that students
are familiar with basic statistics (common probability distributions
like the normal, Poisson, binomial, and gamma; the basics of Maximum
Likelihood (ML) estimation; conditional and bivariate distributions;
how to change variables) but not with advanced probability theory.
The first half of the course will include lectures on the topics below;
the second half will be primarily independent study with the professors
on a topic of the student's choosing (we can help you find one), leading
to a final project to be presented in the final week of the course.
- Stochastic simulation
- Simulating from univariate distributions
- Simulating from multivariate distributions
- Using Markov chains to simulate from multivariate distributions
- Markov Random Field models
This class of model is commonly used for models on spatial grids
(satelite sensing, field experiments, landscape models, etc.).
Models are constructed by specifying the distribution at each
grid location conditionally on the values all other locations.
These models have proven quite useful in image analysis, landscape
ecology, agriculture, and epidemiology --- just to name a few.
- Geostatistical Models
This class of models uses Gaussian random fields
to describe spatially (or temporally) dependent data.
- Point Processes Models
Models to account for the spatial distribution of events
(disease cases, tree locations, IP packets, etc.).