Approximating likelihoods for large spatial data sets

Michael L. Stein*, Zhiyi Chi, Leah J. Welty

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

233 Scopus citations

Abstract

Likelihood methods are often difficult to use with large, irregularly sited spatial data sets, owing to the computational burden. Even for Gaussian models, exact calculations of the likelihood for n observations require O(n 3) operations. Since any joint density can be written as a product of conditional densities based on some ordering of the observations, one way to lessen the computations is to condition on only some of the 'past' observations when computing the conditional densities. We show how this approach can be adapted to approximate the restricted likelihood and we demonstrate how an estimating equations approach allows us to judge the efficacy of the resulting approximation. Previous work has suggested conditioning on those past observations that are closest to the observation whose conditional density we are approximating. Through theoretical, numerical and practical examples, we show that there can often be considerable benefit in conditioning on some distant observations as well.

Original languageEnglish
Pages (from-to)275-296
Number of pages22
JournalJournal of the Royal Statistical Society. Series B: Statistical Methodology
Volume66
Issue number2
DOIs
StatePublished - 2004

Keywords

  • Chlorophyll fluorescence
  • Estimating equations
  • Restricted maximum likelihood
  • Variogram estimation

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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