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  "body": "\n## Summary\n\nA Markov random field is a family of random variables indexed by the vertices of an undirected [[graph|00C0BR7D7H]].\nEach variable depends on the others only through its neighbours.\nIt is the undirected kind of [[graphical model|Q3FQAD1BXG]].\nBy the [[Hammersley–Clifford theorem|K07QH8EKD0]], positive Markov random fields are exactly the distributions that factor over the [[cliques|0BYX1D7C2E]] of the graph.\nThe Ising model and many models in image analysis are Markov random fields.\n\n## Explanations\n\n### L1 human\n\nThink of the pixels of a black and white image, each joined to its four neighbours.\nIn a Markov random field, once the colours of the neighbours of a pixel are known, the rest of the image tells nothing more about that pixel.\nThis captures the idea that nearby pixels tend to agree while far pixels interact only through the pixels between them.\nThe same picture works for spins in a magnet, which is the Ising model.\n",
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