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Bayesian modelling of spatial compositional data

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  • Håkon Tjelmeland
  • Kjetill Vassmo Lund

Abstract

Compositional data are vectors of proportions, specifying fractions of a whole. Aitchison (1986) defines logistic normal distributions for compositional data by applying a logistic transformation and assuming the transformed data to be multi- normal distributed. In this paper we generalize this idea to spatially varying logistic data and thereby define logistic Gaussian fields. We consider the model in a Bayesian framework and discuss appropriate prior distributions. We consider both complete observations and observations of subcompositions or individual proportions, and discuss the resulting posterior distributions. In general, the posterior cannot be analytically handled, but the Gaussian base of the model allows us to define efficient Markov chain Monte Carlo algorithms. We use the model to analyse a data set of sediments in an Arctic lake. These data have previously been considered, but then without taking the spatial aspect into account.

Suggested Citation

  • Håkon Tjelmeland & Kjetill Vassmo Lund, 2003. "Bayesian modelling of spatial compositional data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 30(1), pages 87-100.
    • Handle: RePEc:taf:japsta:v:30:y:2003:i:1:p:87-100
    DOI: 10.1080/0266476022000018547
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    Cited by:

    1. J. Haslett & M. Whiley & S. Bhattacharya & M. Salter‐Townshend & Simon P. Wilson & J. R. M. Allen & B. Huntley & F. J. G. Mitchell, 2006. "Bayesian palaeoclimate reconstruction," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 169(3), pages 395-438, July.

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