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首页> 外文期刊>Journal of Statistical Physics >Partially Observed Markov Random Fields Are Variable Neighborhood Random Fields
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Partially Observed Markov Random Fields Are Variable Neighborhood Random Fields

机译：部分观测的马尔可夫随机场是可变邻域随机场

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摘要

The present paper has two goals. First to present a natural example of a new class of random fields which are the variable neighborhood random fields. The example we consider is a partially observed nearest neighbor binary Markov random field. The second goal is to establish sufficient conditions ensuring that the variable neighborhoods are almost surely finite. We discuss the relationship between the almost sure finiteness of the interaction neighborhoods and the presence/absence of phase transition of the underlying Markov random field. In the case where the underlying random field has no phase transition we show that the finiteness of neighborhoods depends on a specific relation between the noise level and the minimum values of the one-point specification of the Markov random field. The case in which there is phase transition is addressed in the frame of the ferromagnetic Ising model. We prove that the existence of infinite interaction neighborhoods depends on the phase.
机译：本论文有两个目标。首先给出一个新的随机字段类别的自然示例，它们是可变邻域随机字段。我们考虑的示例是部分观测到的最近邻二进制马尔可夫随机场。第二个目标是建立足够的条件，以确保可变邻域几乎肯定是有限的。我们讨论了相互作用邻域的几乎确定的有限性与基础马尔可夫随机场的相变存在/不存在之间的关系。在下面的随机场没有相变的情况下，我们表明邻域的有限性取决于噪声水平与马尔可夫随机场的单点规格最小值之间的特定关系。在铁磁伊辛模型的框架中解决了存在相变的情况。我们证明了无限相互作用邻域的存在取决于相位。

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