Pseudo-likelihood approach for pair potential estimation of Gibbs processes

This work concentrates on pair potential estimation of unmarked and marked Gibbs point processes through the pseudo-likelihood method. The estimation equations are derived for discretely and continuously marked Gibbs processes on bounded subsets of Rd and applied to the analysis of three empirical d...

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Päätekijä: Särkkä, Aila
Aineistotyyppi: Väitöskirja
Kieli:eng
Julkaistu: 1993
Aiheet:
Linkit: https://jyx.jyu.fi/handle/123456789/103855
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author Särkkä, Aila
author_facet Särkkä, Aila Särkkä, Aila
author_sort Särkkä, Aila
datasource_str_mv jyx
description This work concentrates on pair potential estimation of unmarked and marked Gibbs point processes through the pseudo-likelihood method. The estimation equations are derived for discretely and continuously marked Gibbs processes on bounded subsets of Rd and applied to the analysis of three empirical data. This experimentation shows that the pseudo-likelihood method can fail: it leads to overestimation probably because of strong interactions between the objects. The method appears to be sensitive to outlying orservations. Several techniques to detect outlying observations are suggested and bias corrections are discussed. Connection between the pseudo-likelihood and the Takacs-Fiksel estimation methods is shown for marked point processes with a general pair potential function. As a consequence, it is proved that the pseudo-likelihood method can be applied also to modelling data collected through field measurements. As an application to practical forestry, interactions between trees in pine and spruce forests in Central Finland are studied using data consisting of so-called INKA sample plots collected by The Finnish Forest Research Institute.
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The estimation equations are derived for discretely and continuously marked Gibbs processes on bounded subsets of Rd and applied to the analysis of three empirical data. This experimentation shows that the pseudo-likelihood method can fail: it leads to overestimation probably because of strong interactions between the objects. The method appears to be sensitive to outlying orservations. Several techniques to detect outlying observations are suggested and bias corrections are discussed. Connection between the pseudo-likelihood and the Takacs-Fiksel estimation methods is shown for marked point processes with a general pair potential function. As a consequence, it is proved that the pseudo-likelihood method can be applied also to modelling data collected through field measurements. 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publishDate 1993
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spellingShingle Särkkä, Aila Pseudo-likelihood approach for pair potential estimation of Gibbs processes tilastotiede estimointi pseudo-likelihood Takacs-Fiksel method
title Pseudo-likelihood approach for pair potential estimation of Gibbs processes
title_full Pseudo-likelihood approach for pair potential estimation of Gibbs processes
title_fullStr Pseudo-likelihood approach for pair potential estimation of Gibbs processes Pseudo-likelihood approach for pair potential estimation of Gibbs processes
title_full_unstemmed Pseudo-likelihood approach for pair potential estimation of Gibbs processes Pseudo-likelihood approach for pair potential estimation of Gibbs processes
title_short Pseudo-likelihood approach for pair potential estimation of Gibbs processes
title_sort pseudo likelihood approach for pair potential estimation of gibbs processes
title_txtP Pseudo-likelihood approach for pair potential estimation of Gibbs processes
topic tilastotiede estimointi pseudo-likelihood Takacs-Fiksel method
topic_facet Takacs-Fiksel method estimointi pseudo-likelihood tilastotiede
url https://jyx.jyu.fi/handle/123456789/103855 http://www.urn.fi/URN:ISBN:978-952-86-0845-5
work_keys_str_mv AT särkkäaila pseudolikelihoodapproachforpairpotentialestimationofgibbsprocesses