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Modelling spatially correlated data via mixtures: a Bayesian approach

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  • Carmen Fernández
  • Peter J. Green

Abstract

Summary. The paper develops mixture models for spatially indexed data. We confine attention to the case of finite, typically irregular, patterns of points or regions with prescribed spatial relationships, and to problems where it is only the weights in the mixture that vary from one location to another. Our specific focus is on Poisson‐distributed data, and applications in disease mapping. We work in a Bayesian framework, with the Poisson parameters drawn from gamma priors, and an unknown number of components. We propose two alternative models for spatially dependent weights, based on transformations of autoregressive Gaussian processes: in one (the logistic normal model), the mixture component labels are exchangeable; in the other (the grouped continuous model), they are ordered. Reversible jump Markov chain Monte Carlo algorithms for posterior inference are developed. Finally, the performances of both of these formulations are examined on synthetic data and real data on mortality from a rare disease.

Suggested Citation

  • Carmen Fernández & Peter J. Green, 2002. "Modelling spatially correlated data via mixtures: a Bayesian approach," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 805-826, October.
    • Handle: RePEc:bla:jorssb:v:64:y:2002:i:4:p:805-826
    DOI: 10.1111/1467-9868.00362
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    References listed on IDEAS

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    1. Green P.J. & Richardson S., 2002. "Hidden Markov Models and Disease Mapping," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 1055-1070, December.
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    1. repec:dau:papers:123456789/9572 is not listed on IDEAS
    2. Håvard Rue & Ingelin Steinsland & Sveinung Erland, 2004. "Approximating hidden Gaussian Markov random fields," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(4), pages 877-892, November.
    3. Congdon, Peter, 2007. "Mixtures of spatial and unstructured effects for spatially discontinuous health outcomes," Computational Statistics & Data Analysis, Elsevier, vol. 51(6), pages 3197-3212, March.
    4. Deb, Soudeep & Karmakar, Sayar, 2023. "A novel spatio-temporal clustering algorithm with applications on COVID-19 data from the United States," Computational Statistics & Data Analysis, Elsevier, vol. 188(C).
    5. Vidal Rodeiro, Carmen L. & Lawson, Andrew B., 2005. "An evaluation of the edge effects in disease map modelling," Computational Statistics & Data Analysis, Elsevier, vol. 49(1), pages 45-62, April.
    6. Lei Xu & Timothy D. Johnson & Thomas E. Nichols & Derek E. Nee, 2009. "Modeling Inter-Subject Variability in fMRI Activation Location: A Bayesian Hierarchical Spatial Model," Biometrics, The International Biometric Society, vol. 65(4), pages 1041-1051, December.
    7. Vinicius Mayrink & Dani Gamerman, 2009. "On computational aspects of Bayesian spatial models: influence of the neighboring structure in the efficiency of MCMC algorithms," Computational Statistics, Springer, vol. 24(4), pages 641-669, December.
    8. Luc Anselin & Pedro Amaral, 2024. "Endogenous spatial regimes," Journal of Geographical Systems, Springer, vol. 26(2), pages 209-234, April.
    9. Jan Povala & Seppo Virtanen & Mark Girolami, 2020. "Burglary in London: insights from statistical heterogeneous spatial point processes," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 69(5), pages 1067-1090, November.
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    11. M. Rufo & J. Martín & C. Pérez, 2006. "Bayesian analysis of finite mixture models of distributions from exponential families," Computational Statistics, Springer, vol. 21(3), pages 621-637, December.

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