2009-10 Program on Space-time Analysis for Environmental Mapping, Epidemiology and Climate Change

Institute for Mathematics Applied to Geosciences (IMAGe)

Summer School on Spatial Statistics

General Information
Course Contents
Prerequisites
Application
Additional Information
Schedule

Organizers/Instructors

Sudipto Banerjee (U. Minnesota), Reinhard Furrer (U. Zurich), Doug Nychka (National Center for Atmospheric Research), and Stephen Sain (National Center for Atmospheric Research)

General Information

Determining the air quality at an unmonitored location, characterizing the mean summer temperature and precipitation over a region or quantifying the changing incidence of a disease across an urban area are examples where a function of interest depends on irregular and limited observations. Prediction and scientific understanding of environmental and epidemiology data often requires estimating a smooth curve or surface over space that describes an environmental process or summarizes complex structure. Moreover, drawing inferences from the estimate requires measures of uncertainty for the unknown function. This course will combine ideas from geostatistics, smoothing, and Bayesian inference to tackle these problems.

An important component of the lectures is the use of contributed packages for the R statistical environment (www.r-project.org) for hands-on experience with these methods, analyzing spatial data and practice in problem solving. In addition these open source R packages (e.g. spBayes, fields and spam) provide insight in the computational framework for function fitting and the facility to handle multivariate or large environmental datasets. The overall theme of this course is to illustrate how statistical science requires a blending of the scientific context, statistical modeling and statistical computing to reach a useful solution.

Course Contents

The first part of the course explains a common framework for spatial statistics and splines using ridge regression. This correspondence provides a common computational approach and leads to easy to use methods for Kriging and thin-plate splines. Several case studies will illustrate how these methods work in practice and the class is encouraged to modify the related R code and scripts to explore variations in the analysis. The second part of the course considers multivariate spatial responses and large spatial data sets. Building from the basic methods, these topics extend the R packages either through multivariate covariance functions or sparse matrix methods. The final part of the course will introduce a Bayesian framework for spatial models that not only provides a comprehensive quantification of the uncertainty of the spatial analysis but also provides efficient strategies for dimension reduction in hierarchical models.

In particular, the last part of the course will concentrate on Bayesian methods for spatial epidemiology and other public health applications. Here, data often arise as aggregated summaries over regions (e.g. counts or rates of disease incidence, mortality etc.) and the spatial referencing is done with respect to regions (e.g. counties, census-tracts, zip-codes etc.). While geostatistical models can still be used to model such data, spatial models can now build associations based upon conditional dependencies over the underlying neighborhood structures. These lead to Simultaneously AutoRegressive (SAR) and Conditionally AutoRegressive (CAR) models. Such models will be explained along with existing software resources in R (the spdep and BRUGS packages).

An important part of the course will be blocks of time where students are encouraged to work independently or in teams on the analysis of spatial or space/time datasets. This will not only build skill in statistical computing and the R language but will also be an opportunity for informal presentations and collaboration with other students.

Prerequisites

Familiarity with statistical linear models, multivariate regression and matrix algebra. A first course in Bayesian statistics is also strongly recommended. A laptop with wireless connectivity is strongly recommended, although some desktop computers will be available for those without a laptop.

Application

The application deadline is May 22, 2009. Note, however, that workshop capacity might be reached before this deadline.

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Additional Information

Financial support for travel expenses, subsistence and lodging will be provided for all attendees. Due to space considerations, participation is restricted and will be offered to approximately 30 individuals selected from the applicant pool.

Participants are expected to arrive for the summer school on Monday, July 27, 2009 and remain in continuous attendance until 12:00 pm on Saturday, August 1, 2009.

Schedule

TBA

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