ABC Shadow algorithm: a tool for statistical analysis of spatial patterns |
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| Authors: | Radu S. Stoica Anne Philippe Pablo Gregori Jorge Mateu |
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| Affiliation: | 1.Laboratoire Paul Painlevé,Université de Lille,Villeneuve d’Ascq Cedex,France;2.Institut de Mécanique Céleste et Calcul des Ephémérides (IMCCE),Observatoire de Paris,Paris,France;3.Laboratoire de Mathématiques Jean Leray, ANJA INRIA Rennes Bretagne Atlantique,Université de Nantes,Nantes Cedex 3,France;4.Departamento de Matemáticas, Instituto Universitario de Matemáticas y Aplicaciones de Castellón (IMAC),Universitat Jaume I de Castellón,Castellón,Spain |
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| Abstract: | This paper presents an original ABC algorithm, ABC Shadow, that can be applied to sample posterior densities that are continuously differentiable. The proposed algorithm solves the main condition to be fulfilled by any ABC algorithm, in order to be useful in practice. This condition requires enough samples in the parameter space region, induced by the observed statistics. The algorithm is tuned on the posterior of a Gaussian model which is entirely known, and then, it is applied for the statistical analysis of several spatial patterns. These patterns are issued or assumed to be outcomes of point processes. The considered models are: Strauss, Candy and area-interaction. |
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