Journal
ANNUAL REVIEW OF STATISTICS AND ITS APPLICATION, VOL 4
Volume 4, Issue -, Pages 245-266Publisher
ANNUAL REVIEWS
DOI: 10.1146/annurev-statistics-060116-054155
Keywords
big spatial data; data assimilation; data fusion; Gaussian processes; integrated nested Laplace approximation; Markov chain Monte Carlo; multivariate spatial processes; spatiotemporal processes
Funding
- NIEHS NIH HHS [R01 ES027027] Funding Source: Medline
- NIGMS NIH HHS [RC1 GM092400] Funding Source: Medline
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The most prevalent spatial data setting is, arguably, that of so-called geostatistical data, data that arise as random variables observed at fixed spatial locations. Collection of such data in space and in time has grown enormously in the past two decades. With it has grown a substantial array of methods to analyze such data. Here, we attempt a review of a fully model-based perspective for such data analysis, the approach of hierarchical modeling fitted within a Bayesian framework. The benefit, as with hierarchical Bayesian modeling in general, is full and exact inference, with proper assessment of uncertainty. Geostatistical modeling includes univariate and multivariate data collection at sites, continuous and categorical data at sites, static and dynamic data at sites, and datasets over very large numbers of sites and long periods of time. Within the hierarchical modeling framework, we offer a review of the current state of the art in these settings.
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