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 Electronic Journal of Statistics > Vol. 2 (2008) open journal systems 


Spatial modelling for mixed-state observations

Cécile Hardouin, SAMOS-MATISSE-Centre d'Économie de la Sorbonne,
Jian-Feng Yao, IRMAR, Université de Rennes 1


Abstract
In several application fields like daily pluviometry data modelling, or motion analysis from image sequences, observations contain two components of different nature. A first part is made with discrete values accounting for some symbolic information and a second part records a continuous (real-valued) measurement. We call such type of observations ``mixed-state observations". This paper introduces spatial models suited for the analysis of these kinds of data. We consider multi-parameter auto-models whose local conditional distributions belong to a mixed state exponential family. Specific examples with exponential distributions are detailed, and we present some experimental results for modelling motion measurements from video sequences.

AMS 2000 subject classifications: Primary 62H05, 62E10; secondary 62M40.

Keywords: Multivariate analysis, Distribution theory, Mixed-state variables, Auto-models, Spatial cooperation, Markov random fields.

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Hardouin, Cécile, Yao, Jian-Feng, Spatial modelling for mixed-state observations, Electronic Journal of Statistics, 2, (2008), 213-233 (electronic). DOI: 10.1214/08-EJS173.

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Electronic Journal of Statistics. ISSN: 1935-7524