State estimation for random closed sets

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Abstract

State estimation entails the estimation of an unobserved random closed set from (partial) observation of an associated random set. Examples include edge effect correction, cluster detection, filtering and prediction. We focus on inference for random sets based on points sampled on its boundary. Such data are subject to mis-alignment and noise. First, we ignore mis-alignment and discuss maximum likelihood estimation of the model and noise parameters in the Fourier domain. We estimate the unknown curve by back-transformation and derive the expectation of the integrated squared error. Then, we model mis-alignment by means of a shifted parametric diffeomorphism and minimise a suitable objective function simultaneously over the unknown curve and the mis-alignment parameters.
Original languageUndefined
Title of host publicationSpatial Statistics 2015: Emerging Patterns
EditorsAlfred Stein, Denis Allard
PublisherElsevier
Pages70-74
Number of pages5
DOIs
Publication statusPublished - 9 Jun 2015

Publication series

NameProcedia Environmental Sciences
PublisherElsevier
Volume27
ISSN (Print)1878-0296
ISSN (Electronic)1878-0296

Keywords

  • EWI-26225
  • Spectral analysis
  • State estimation
  • METIS-312698
  • Random closed set
  • IR-97077
  • Missing data

Cite this

van Lieshout, M. N. M. (2015). State estimation for random closed sets. In A. Stein, & D. Allard (Eds.), Spatial Statistics 2015: Emerging Patterns (pp. 70-74). (Procedia Environmental Sciences; Vol. 27). Elsevier. https://doi.org/10.1016/j.proenv.2015.07.097
van Lieshout, Maria Nicolette Margaretha. / State estimation for random closed sets. Spatial Statistics 2015: Emerging Patterns. editor / Alfred Stein ; Denis Allard. Elsevier, 2015. pp. 70-74 (Procedia Environmental Sciences).
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van Lieshout, MNM 2015, State estimation for random closed sets. in A Stein & D Allard (eds), Spatial Statistics 2015: Emerging Patterns. Procedia Environmental Sciences, vol. 27, Elsevier, pp. 70-74. https://doi.org/10.1016/j.proenv.2015.07.097

State estimation for random closed sets. / van Lieshout, Maria Nicolette Margaretha.

Spatial Statistics 2015: Emerging Patterns. ed. / Alfred Stein; Denis Allard. Elsevier, 2015. p. 70-74 (Procedia Environmental Sciences; Vol. 27).

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

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AB - State estimation entails the estimation of an unobserved random closed set from (partial) observation of an associated random set. Examples include edge effect correction, cluster detection, filtering and prediction. We focus on inference for random sets based on points sampled on its boundary. Such data are subject to mis-alignment and noise. First, we ignore mis-alignment and discuss maximum likelihood estimation of the model and noise parameters in the Fourier domain. We estimate the unknown curve by back-transformation and derive the expectation of the integrated squared error. Then, we model mis-alignment by means of a shifted parametric diffeomorphism and minimise a suitable objective function simultaneously over the unknown curve and the mis-alignment parameters.

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KW - METIS-312698

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van Lieshout MNM. State estimation for random closed sets. In Stein A, Allard D, editors, Spatial Statistics 2015: Emerging Patterns. Elsevier. 2015. p. 70-74. (Procedia Environmental Sciences). https://doi.org/10.1016/j.proenv.2015.07.097