Symmetry, stability, and spatio-temporal dependence in multinomial Markov random field models

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2022-12
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McClernon, Kellie L
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Kaiser, Mark S
Nordman, Daniel
Genschel, Ulrike
Roy, Vivekananda
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Statistics
Abstract
Recent developments in Markov random field models for multinomials fail to treat the critical lack of symmetry among the categories when spatial dependence is incorporated. We demonstrate that the traditional full-rank parameterization exhibits lack of symmetry and recommend a new parameterization - the symmetric. We establish important model properties and regions of model stability for both Markov field models. Lastly, we extend the symmetric Markov random field model to include both temporal and spatial dependence through two distinct formulations to illustrate the difference among the resulting dependence structures.
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