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On the MLE for a spatial point pattern

Published online by Cambridge University Press:  01 July 2016

Francisco Montes
Affiliation:
Universitat de València
Jorge Mateu
Affiliation:
Universitat Jaume 1

Extract

Parameter estimation for a two-dimensional point pattern is difficult because most of the available stochastic models have intractable likelihoods ([2]). An exception is the class of Gibbs or Markov point processes ([1], [5]), where the likelihood typically forms an exponential family and is given explicitly up to a normalising constant. However, the latter is not known analytically, so parameter estimates must be based on approximations ([3], [6], [7]). In this paper we present comparisons amongst the different techniques available in the literature to obtain an approximation of the maximum likelihood estimate (MLE). Two stochastic methods are specifically illustrated: a Newton-Raphson algorithm ([7]) and the Robbins-Monro procedure ([8]). We use a very simple point process model, the Strauss process ([4]), to test and compare those approximations.

Type
Stochastic Geometry and Statistical Applications
Copyright
Copyright © Applied Probability Trust 1996 

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References

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