Probabilistic Context Neighborhood Model for Lattices
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866911767436722176 |
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| author | Magalhaes, Debora F. Piroutek, Aline M. Duarte, Denise Alves, Caio |
| author_facet | Magalhaes, Debora F. Piroutek, Aline M. Duarte, Denise Alves, Caio |
| contents | We present the Probabilistic Context Neighborhood model designed for two-dimensional lattices as a variation of a Markov Random Field assuming discrete values. In this model, the neighborhood structure has a fixed geometry but a variable order, depending on the neighbors' values. Our model extends the Probabilistic Context Tree model, originally applicable to one-dimensional space. It retains advantageous properties, such as representing the dependence neighborhood structure as a graph in a tree format, facilitating an understanding of model complexity. Furthermore, we adapt the algorithm used to estimate the Probabilistic Context Tree to estimate the parameters of the proposed model. We illustrate the accuracy of our estimation methodology through simulation studies. Additionally, we apply the Probabilistic Context Neighborhood model to spatial real-world data, showcasing its practical utility. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_16598 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Probabilistic Context Neighborhood Model for Lattices Magalhaes, Debora F. Piroutek, Aline M. Duarte, Denise Alves, Caio Methodology 62M15, 62M30 We present the Probabilistic Context Neighborhood model designed for two-dimensional lattices as a variation of a Markov Random Field assuming discrete values. In this model, the neighborhood structure has a fixed geometry but a variable order, depending on the neighbors' values. Our model extends the Probabilistic Context Tree model, originally applicable to one-dimensional space. It retains advantageous properties, such as representing the dependence neighborhood structure as a graph in a tree format, facilitating an understanding of model complexity. Furthermore, we adapt the algorithm used to estimate the Probabilistic Context Tree to estimate the parameters of the proposed model. We illustrate the accuracy of our estimation methodology through simulation studies. Additionally, we apply the Probabilistic Context Neighborhood model to spatial real-world data, showcasing its practical utility. |
| title | Probabilistic Context Neighborhood Model for Lattices |
| topic | Methodology 62M15, 62M30 |
| url | https://arxiv.org/abs/2401.16598 |