部分观测马尔可夫随机场是变邻域随机场
Partially observed Markov random fields are variable neighborhood random fields
摘要：
本文件有两个目标。首先给出一类新的随机场的自然例子，即变邻域随机场。我们考虑的例子是一个部分观测的最近邻二进制马尔可夫随机场。第二个目标是建立充分条件，确保变量邻域几乎必然有限。讨论了相互作用邻域的几乎必然有限性与马尔可夫随机场相变的存在与否之间的关系。在基本的随机场没有相变的情况下，我们表明，有限的邻域依赖于一个特定的关系之间的噪声水平和最小值的一点规格的马尔可夫随机场。在铁磁伊辛模型的框架中，有相变的情况下解决。我们证明了无限相互作用邻域的存在依赖于相位。
英文摘要：
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.
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