Spatial Statistics Software

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The following lists some software available for fitting spatial models of various sorts, with an emphasis on spatial smoothing.

Smoothing of location-specific data
The Fields software package for R implements thin plate spline fitting and kriging. (Available from the R archive.)
The geoR and geoS packages for R and S-plus, respectively, implement classical and Bayesian implementations of kriging.
The mgcv package for R fits additive models with the ability to model spatial surfaces as nonparametric smooth two-dimensional surfaces.
The Semipar package for S-plus (an R library is underconstruction) fits spatial surfaces using a mixed models framework.
Free-knot spline models for nonparametric regression with arbitrary covariates can fit spatial surfaces as a special case. This code is in Matlab.

Markov random field models
Markov random field models are designed for data aggregated into regions; they smooth data based on the neighborhood structure of the regions. The GeoBUGS software package has been developed by a team at the Department of Epidemiology and Public Health of Imperial College at St Mary's Hospital, London. It is an add-on to WinBUGS that fits spatial models and produces a range of maps as output. Bayesian inference is used to spatially smooth the standardized incidence/mortality ratios using Markov Chain Monte Carlo (MCMC) methods. GeoBUGS implements models for data that are collected within discrete regions (not at the individual level) and smoothing is done based on Markov random field models for the neighborhood structure of the regions relative to each other.

R packages for spatial data
The R project page has a number of other packages useful for spatial modelling of various sorts. A rough categorization of the areas for which the libraries might be useful is:

mapping: mapdata,mapproj,maps,maptools
GIS software interface: GRASS, shapefiles
point process analysis: spatstat, splancs
smoothing: fields, geoR, geoRglm, mgcv
interpolation: akima
general spatial statistics: fields, VR (the spatial component), sgeostat

Other sources of code
Other sources of software include the S archive on statlib, and possibly the Matlab archive.