Spatio-temporal modelling of a Cox point process sampled by a curve, filtering and Inference

Blažena Frcalová; Viktor Beneš

Kybernetika (2009)

  • Volume: 45, Issue: 6, page 912-930
  • ISSN: 0023-5954

Abstract

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The paper deals with Cox point processes in time and space with Lévy based driving intensity. Using the generating functional, formulas for theoretical characteristics are available. Because of potential applications in biology a Cox process sampled by a curve is discussed in detail. The filtering of the driving intensity based on observed point process events is developed in space and time for a parametric model with a background driving compound Poisson field delimited by special test sets. A hierarchical Bayesian model with point process densities yields the posterior. Markov chain Monte Carlo "Metropolis within Gibbs" algorithm enables simultaneous filtering and parameter estimation. Posterior predictive distributions are used for model selection and a numerical example is presented. The new approach to filtering is related to the residual analysis of spatio-temporal point processes.

How to cite

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Frcalová, Blažena, and Beneš, Viktor. "Spatio-temporal modelling of a Cox point process sampled by a curve, filtering and Inference." Kybernetika 45.6 (2009): 912-930. <http://eudml.org/doc/37687>.

@article{Frcalová2009,
abstract = {The paper deals with Cox point processes in time and space with Lévy based driving intensity. Using the generating functional, formulas for theoretical characteristics are available. Because of potential applications in biology a Cox process sampled by a curve is discussed in detail. The filtering of the driving intensity based on observed point process events is developed in space and time for a parametric model with a background driving compound Poisson field delimited by special test sets. A hierarchical Bayesian model with point process densities yields the posterior. Markov chain Monte Carlo "Metropolis within Gibbs" algorithm enables simultaneous filtering and parameter estimation. Posterior predictive distributions are used for model selection and a numerical example is presented. The new approach to filtering is related to the residual analysis of spatio-temporal point processes.},
author = {Frcalová, Blažena, Beneš, Viktor},
journal = {Kybernetika},
keywords = {Cox point process; filtering; spatio-temporal process; Cox point process; filtering; spatio-temporal process},
language = {eng},
number = {6},
pages = {912-930},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Spatio-temporal modelling of a Cox point process sampled by a curve, filtering and Inference},
url = {http://eudml.org/doc/37687},
volume = {45},
year = {2009},
}

TY - JOUR
AU - Frcalová, Blažena
AU - Beneš, Viktor
TI - Spatio-temporal modelling of a Cox point process sampled by a curve, filtering and Inference
JO - Kybernetika
PY - 2009
PB - Institute of Information Theory and Automation AS CR
VL - 45
IS - 6
SP - 912
EP - 930
AB - The paper deals with Cox point processes in time and space with Lévy based driving intensity. Using the generating functional, formulas for theoretical characteristics are available. Because of potential applications in biology a Cox process sampled by a curve is discussed in detail. The filtering of the driving intensity based on observed point process events is developed in space and time for a parametric model with a background driving compound Poisson field delimited by special test sets. A hierarchical Bayesian model with point process densities yields the posterior. Markov chain Monte Carlo "Metropolis within Gibbs" algorithm enables simultaneous filtering and parameter estimation. Posterior predictive distributions are used for model selection and a numerical example is presented. The new approach to filtering is related to the residual analysis of spatio-temporal point processes.
LA - eng
KW - Cox point process; filtering; spatio-temporal process; Cox point process; filtering; spatio-temporal process
UR - http://eudml.org/doc/37687
ER -

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