Statistical Issues in Monitoring the EnvironmentOct. 22-24, 2008

Short Course: Estimating curves and surfaces from environmental data

October 22, ML Main Seminar Room, NCAR

The one-day short course covers the analysis of environmental data that are often spatially and/or temporally correlated. The instructors are renowned researchers with rich experience in modeling and analyzing environmental data. The R packages fields and spam will be introduced and illustrated through real examples and hands-on activities. A laptop with wireless connectivity and the current version of R with the fields and spam packages installed is strongly recommended.

Instructors: Reinhard Furrer, Colorado School of Mines; Doug Nychka and Stephan Sain, National Center for Atmospheric Research.

Description: Determining the air quality at an unmonitored location, characterizing the mean summer temperature and precipitation over a spatial domain or relating soil properties to bulk composition are examples where a function of interest depends on irregular and limited observations. Prediction and scientific understanding of environmental data often require estimating a smooth curve or surface that describes an environmental process or summarizes complex structure. Moreover, drawing inferences from this 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 the fields and spam contributed packages for the R statistical computing environment for hands-on experience with these methods. In addition, these R packages provide insight to the computational framework for function fitting and the facility to handle multivariate or large environmental datasets.

The first part of the course explains a common framework for spatial statistics and splines using ridge regression. This correspondence provides the common computational approach used throughout fields and leads to easy-to-use methods for Kriging and thin-plate splines. Several case studies illustrate how these methods work in practice and the class is encouraged to modify the R code to explore variations in the analysis. The second part of the course considers multivariate responses and large spatial data sets. Building from the basic methods, these lectures extend the fields functions either through multivariate covariance functions or sparse matrix methods.


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