Bernoulli

  • Bernoulli
  • Volume 19, Number 3 (2013), 905-930.

Variational estimators for the parameters of Gibbs point process models

Adrian Baddeley and David Dereudre

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Abstract

This paper proposes a new estimation technique for fitting parametric Gibbs point process models to a spatial point pattern dataset. The technique is a counterpart, for spatial point processes, of the variational estimators for Markov random fields developed by Almeida and Gidas. The estimator does not require the point process density to be hereditary, so it is applicable to models which do not have a conditional intensity, including models which exhibit geometric regularity or rigidity. The disadvantage is that the intensity parameter cannot be estimated: inference is effectively conditional on the observed number of points. The new procedure is faster and more stable than existing techniques, since it does not require simulation, numerical integration or optimization with respect to the parameters.

Article information

Source
Bernoulli, Volume 19, Number 3 (2013), 905-930.

Dates
First available in Project Euclid: 26 June 2013

Permanent link to this document
https://projecteuclid.org/euclid.bj/1372251147

Digital Object Identifier
doi:10.3150/12-BEJ419

Mathematical Reviews number (MathSciNet)
MR3079300

Zentralblatt MATH identifier
1273.62203

Keywords
Campbell measure Gibbs point process non-hereditary interaction pseudolikelihood spatial statistics variational estimator

Citation

Baddeley, Adrian; Dereudre, David. Variational estimators for the parameters of Gibbs point process models. Bernoulli 19 (2013), no. 3, 905--930. doi:10.3150/12-BEJ419. https://projecteuclid.org/euclid.bj/1372251147


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