Fully Bayesian approach to image restoration with an application in biogeography.

*(English)*Zbl 0825.62413Summary: 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.

##### MSC:

62F15 | Bayesian inference |

62C12 | Empirical decision procedures; empirical Bayes procedures |

62M30 | Inference from spatial processes |

62P99 | Applications of statistics |