Model-based geostatistics

P. J. Diggle, J. A. Tawn, R. A. Moyeed

Research output: Contribution to journalArticle

Abstract

Conventional geostatistical methodology solves the problem of predicting the realized value of a linear functional of a Gaussian spatial stochastic process S(x) based on observations Yi = S(xi) + Zi at sampling locations xi, where the Zi are mutually independent, zero-mean Gaussian random variables. We describe two spatial applications for which Gaussian distributional assumptions are clearly inappropriate. The first concerns the assessment of residual contamination from nuclear weapons testing on a South Pacific island, in which the sampling method generates spatially indexed Poisson counts conditional on an unobserved spatially varying intensity of radioactivity; we conclude that a conventional geostatistical analysis oversmooths the data and underestimates the spatial extremes of the intensity. The second application provides a description of spatial variation in the risk of campylobacter infections relative to other enteric infections in part of north Lancashire and south Cumbria. For this application, we treat the data as binomial counts at unit postcode locations, conditionally on an unobserved relative risk surface which we estimate. The theoretical framework for our extension of geostatistical methods is that, conditionally on the unobserved process S(x), observations at sample locations xi form a generalized linear model with the corresponding values of S(xi) appearing as an offset term in the linear predictor. We use a Bayesian inferential framework, implemented via the Markov chain Monte Carlo method, to solve the prediction problem for non-linear functionals of S(x), making a proper allowance for the uncertainty in the estimation of any model parameters.

Original languageEnglish (US)
Pages (from-to)299-325
Number of pages27
JournalJournal of the Royal Statistical Society. Series C: Applied Statistics
Volume47
Issue number3
StatePublished - 1998
Externally publishedYes

Keywords

  • Generalized linear mixed model
  • Geostatistics
  • Kriging
  • Markov chain Monte Carlo method
  • Spatial prediction

ASJC Scopus subject areas

  • Mathematics(all)
  • Statistics and Probability

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  • Cite this

    Diggle, P. J., Tawn, J. A., & Moyeed, R. A. (1998). Model-based geostatistics. Journal of the Royal Statistical Society. Series C: Applied Statistics, 47(3), 299-325.