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Statistics and Computing

, Volume 27, Issue 5, pp 1225–1238 | Cite as

ABC Shadow algorithm: a tool for statistical analysis of spatial patterns

  • Radu S. StoicaEmail author
  • Anne Philippe
  • Pablo Gregori
  • Jorge Mateu
Article

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.

Keywords

Approximate Bayesian computation Computational methods in Markov chains Maximum likelihood estimation Point processes Spatial pattern analysis 

Notes

Acknowledgments

This work was initiated during stays of the first author at University Jaume I and INRA Avignon. The first author is grateful to D. Allard, Yu. Davydov, M. N. M. van Lieshout, J. Møller, E. Saar and the members of the Working Group “Stochastic Geometry” of the University of Lille, for useful comments and discussions. The work of the first author was partially supported by the GDR GEOSTO project. P. Gregori and J. Mateu were supported by Grants P1-1B2012-52 and MTM2013-43917-P.

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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Radu S. Stoica
    • 1
    • 2
    Email author
  • Anne Philippe
    • 3
  • Pablo Gregori
    • 4
  • Jorge Mateu
    • 4
  1. 1.Laboratoire Paul PainlevéUniversité de LilleVilleneuve d’Ascq CedexFrance
  2. 2.Institut de Mécanique Céleste et Calcul des Ephémérides (IMCCE)Observatoire de ParisParisFrance
  3. 3.Laboratoire de Mathématiques Jean Leray, ANJA INRIA Rennes Bretagne AtlantiqueUniversité de NantesNantes Cedex 3France
  4. 4.Departamento de Matemáticas, Instituto Universitario de Matemáticas y Aplicaciones de Castellón (IMAC)Universitat Jaume I de CastellónCastellónSpain

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