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Binary probability maps using a hidden conditional autoregressive Gaussian process with an application to Finnish common toad data

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  • I. S. Weir
  • A. N. Pettitt

Abstract

The Finnish common toad data of Heikkinen and Hogmander are reanalysed using an alternative fully Bayesian model that does not require a pseudolikelihood approximation and an alternative prior distribution for the true presence or absence status of toads in each 10 km×10 km square. Markov chain Monte Carlo methods are used to obtain posterior probability estimates of the square‐specific presences of the common toad and these are presented as a map. The results are different from those of Heikkinen and Hogmander and we offer an explanation in terms of the prior used for square‐specific presence of the toads. We suggest that our approach is more faithful to the data and avoids unnecessary confounding of effects. We demonstrate how to extend our model efficiently with square‐specific covariates and illustrate this by introducing deterministic spatial changes.

Suggested Citation

  • I. S. Weir & A. N. Pettitt, 2000. "Binary probability maps using a hidden conditional autoregressive Gaussian process with an application to Finnish common toad data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 49(4), pages 473-484.
    • Handle: RePEc:bla:jorssc:v:49:y:2000:i:4:p:473-484
    DOI: 10.1111/1467-9876.00206
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    Cited by:

    1. Samuel D. Oman & Victoria Landsman & Yohay Carmel & Ronen Kadmon, 2007. "Analyzing Spatially Distributed Binary Data Using Independent-Block Estimating Equations," Biometrics, The International Biometric Society, vol. 63(3), pages 892-900, September.
    2. Miller, Jennifer & Franklin, Janet & Aspinall, Richard, 2007. "Incorporating spatial dependence in predictive vegetation models," Ecological Modelling, Elsevier, vol. 202(3), pages 225-242.
    3. Marbac, Matthieu & Sedki, Mohammed, 2017. "A family of block-wise one-factor distributions for modeling high-dimensional binary data," Computational Statistics & Data Analysis, Elsevier, vol. 114(C), pages 130-145.
    4. Håvard Rue & Sara Martino & Nicolas Chopin, 2009. "Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(2), pages 319-392, April.
    5. Tilman M. Davies & Martin L. Hazelton, 2013. "Assessing minimum contrast parameter estimation for spatial and spatiotemporal log‐Gaussian Cox processes," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 67(4), pages 355-389, November.
    6. Berrett, Candace & Calder, Catherine A., 2012. "Data augmentation strategies for the Bayesian spatial probit regression model," Computational Statistics & Data Analysis, Elsevier, vol. 56(3), pages 478-490.
    7. Stefanie Kalus & Philipp Sämann & Ludwig Fahrmeir, 2014. "Classification of brain activation via spatial Bayesian variable selection in fMRI regression," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 8(1), pages 63-83, March.
    8. Xiaoyu Jiang & David Gold & Eric D. Kolaczyk, 2011. "Network-based Auto-probit Modeling for Protein Function Prediction," Biometrics, The International Biometric Society, vol. 67(3), pages 958-966, September.

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