Unified Geostatistical Modeling for Data Fusion and Spatial Heteroskedasticity with R Package ramps

Spatial data, either areal or geostatistical (point-referenced), are becoming increasingly utilized in the study of many scientific fields due to the accessibility of data monitoring systems and associated datasets. When both types of data are available for the same underlying spatial process, computationally efficient and statistically sound methods are needed for their joint analysis. Markov chain Monte Carlo (MCMC) is a very powerful tool often used for the Bayesian analysis of spatial data. However, its efficiency can be diminished by substantial autocorrelation in values of the model parameters sampled from the posterior distribution. Yan, Cowles, Wang, and Armstrong (2007) recently proposed a reparameterized and marginalized posterior sampling (RAMPS) algorithm which leads to lower autocorrelation in MCMC samples for Bayesian spatiotemporal geostatistical modeling. The RAMPS algorithm has been further extended to a unified framework of linear mixed models (Cowles, Yan, and Smith, 2007) that allows fusion of data obtained at different resolutions (areal and point-referenced) and spatial heteroskedasticity. The general framework also covers cases where prediction at arbitrary sites and non-spatial random effects are needed. This article describes the implementation of the RAMPS algorithm in the R package ramps (Smith, Yan, and Cowles, 2007) and illustrates its use with a synthetic dataset. Existing R packages for geostatistical analysis include fields (Fields Development Team, 2006), geoR (Ribeiro and Diggle, 2001), geoRglm (Christensen and Ribeiro, 2002), gstat (Pebesma and Wesseling, 1998), sgeostat (Majure and Gebhardt, 2007), spatial (Venables and Ripley, 2002), and spBayes (Finley, Banerjee, and Carlin, 2007). The fields, gstat, sgeostat, and spatial packages rely on frequentist kriging for modeling and prediction of geostatistical data. The geoR (and the associated package geoRglm for generalized linear models) and spBayes packages offer routines to fit Bayesian geostatistical models. These packages do not accommodate combined analysis of point-source data and areal data, which is one of the unique features of the ramps package. The spBayes package is not tailored to yield MCMC samples with lower auto-correlations, which may be critically important in analyzing large datasets. The geoR package attains independent posterior samples at the expense of discretizing the prior and posterior densities of two spatial parameters. The starting point for our unified geostatistical model is the basic RAMPS algorithm for point-source data only, described first in Yan et al. (2007). Consider geostatistical