Talk to be held at the workshop on image analysis and spatial statistics in forestry on November 2, 1999 at KVL, Frederiksberg, Denmark

Bayesian Analysis of Point Patterns from Noisy Observations.

Jens Lund (jlund@dina.kvl.dk)
Dept. of Mathematics and Physics, Royal Veterinary and Agricultural University of Denamrk.

A Bayesian analysis of point patterns degraded by thinning, random displacement and superposition of `ghost' points is suggested. Pairwise interaction Gibbs point processes are used as prior models for the unobserved true point pattern, and a Metropolis-Hastings type algorithm is constructed for simulation of the posterior distribution of the unobserved point pattern and associated information. The simulations are then used for estimation of statistical summaries such as the $K$-function, the nearest neighbour distribution function and the empty space statistic for the true point pattern. Analysis of degraded point patterns is relevant in a lot of situations with indirect observations or inverse problems in e.g.~high~level image analysis. We illustrate the method by a forestry example where tree maps are constructed from aerial photographs and the observed tree positions are disturbed by the image analysis process.