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Conditional cyclic Markov random fields

Part of: Stochastic processes Limit theorems

Published online by Cambridge University Press:  01 July 2016

John T. Kent ,
Kanti V. Mardia  and
Alistair N. Walder
John T. Kent*
Affiliation:
University of Leeds
Kanti V. Mardia*
Affiliation:
University of Leeds
Alistair N. Walder*
Affiliation:
University of Leeds
*
* Postal address for all authors: Department of Statistics, University of Leeds, Leeds LS2 9JT, UK.
* Postal address for all authors: Department of Statistics, University of Leeds, Leeds LS2 9JT, UK.
* Postal address for all authors: Department of Statistics, University of Leeds, Leeds LS2 9JT, UK.
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Abstract

Grenander et al. (1991) proposed a conditional cyclic Gaussian Markov random field model for the edges of a closed outline in the plane. In this paper the model is recast as an improper cyclic Gaussian Markov random field for the vertices. The limiting behaviour of this model when the vertices become closely spaced is also described and in particular its relationship with the theory of ‘snakes' (Kass et al. 1987) is established. Applications are given in Grenander et al. (1991), Mardia et al. (1991) and Kent et al. (1992).

Keywords

DEFORMABLE TEMPLATESCYCLIC STATIONARITYLIMITING BEHAVIOURSNAKES

MSC classification

Primary: 60G60: Random fields
Secondary: 60F05: Central limit and other weak theorems

Information

Type
Stochastic Geometry amd Statistical Applications
Information
Advances in Applied Probability , Volume 28 , Issue 1 , March 1996 , pp. 1 - 12
Copyright
Copyright © Applied Probability Trust 1996 

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