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Fully Bayesian Approach to Image Restoration with an Application in Biogeography

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  • Juha Heikkinen
  • Harri Högmander

Abstract

A common method of studying biogeographical ranges is an atlas survey, in which the research area is divided into a square grid and the data consist of the squares where observations occur. Often the observations form only an incomplete map of the true range, and a method is required to decide whether the blank squares indicate true absence or merely a lack of study there. This is essentially an image restoration problem, but it has properties that make the common empirical Bayesian procedures inadequate. Most notably, the observed image is heavily degraded, causing difficulties in the estimation of spatial interaction, and the assessment of reliability of the restoration is emphasized. A fully Bayesian approach is suggested, its implementation and practical properties are discussed and the procedure is applied to data from an atlas survey of Finnish herpetofauna.

Suggested Citation

  • Juha Heikkinen & Harri Högmander, 1994. "Fully Bayesian Approach to Image Restoration with an Application in Biogeography," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 43(4), pages 569-582, December.
    • Handle: RePEc:bla:jorssc:v:43:y:1994:i:4:p:569-582
    DOI: 10.2307/2986258
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    Cited by:

    1. Miller, Jennifer & Franklin, Janet & Aspinall, Richard, 2007. "Incorporating spatial dependence in predictive vegetation models," Ecological Modelling, Elsevier, vol. 202(3), pages 225-242.
    2. Solaiman Afroughi & Soghrat Faghihzadeh & Majid Jafari Khaledi & Mehdi Ghandehari Motlagh & Ebrahim Hajizadeh, 2011. "Analysis of clustered spatially correlated binary data using autologistic model and Bayesian method with an application to dental caries of 3--5-year-old children," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(12), pages 2763-2774, February.

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