Reciprocal properties of random fields on undirected graphs

• We clarify and refine the definition of a reciprocal random field on an undirected graph, with the reciprocal chain as a special case, by introducing four new properties: the factorizing, global, local, and pairwise reciprocal properties, in decreasing order of strength, with respect to a set of nodes delta. They reduce to the better-known Markov properties if 8 is the empty set, or, with the exception of the local property, if delta is a complete set. Conditions for each reciprocal property to imply the next stronger property are derived, and it is shown that, conditionally on the values at a set of nodes delta(0), all four properties are preserved for the subgraph induced by the remaining nodes, with respect to the node set delta \ delta(0). We note that many of the above results are new even for reciprocal chains.

Ämnesord

NATURVETENSKAP  -- Matematik -- Sannolikhetsteori och statistik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Probability Theory and Statistics (hsv//eng)

Nyckelord

Conditional independence; Markov property; random field; reciprocal chain; reciprocal property; undirected graph

Publikations- och innehållstyp

ref (ämneskategori)

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