Bayesian hierarchical models for spatially misaligned data in R

Abstract

Summary: Spatial misalignment occurs when at least one of multiple outcome variables is missing at an observed location. For spatial data, prediction of these missing observations should be informed by within location association among outcomes and by proximate locations where measurements were recorded. This study details and illustrates a Bayesian regression framework for modelling spatially misaligned multivariate data. Particular attention is paid to developing valid probability models capable of estimating parameter posterior distributions and propagating uncertainty through to outcomes' predictive distributions at locations where some or all of the outcomes are not observed. Models and associated software are presented for both Gaussian and non-Gaussian outcomes. Model parameter and predictive inference within the proposed framework is illustrated using a synthetic and forest inventory data set. The proposed Markov chain Monte carlo samplers were written in c++ and leverage R's Foreign Language Interface to call fortran blas (Basic Linear Algebra Subprograms) and lapack (Linear Algebra Package) libraries for efficient matrix computations. The models are implemented in the spMisalignLM and spMisalignGLM functions within the spBayes r package available via the Comprehensive R Archive Network (cran) (http://cran.r-project.org). © 2014 British Ecological Society.