The state of a hidden node is related to the value of its corresponding observed node as well as the states of its neighboring hidden nodes.
the local Markov property of an MRF indicates that a variable is conditionally independent on all other variables given its neighbors: , where ne(v) is the set of neighbors of v, and cl(v) = {v} ∪ ne(v) is the closed neighborhood of v. the state of a node is assumed to statistically depend only upon its hidden node and each of its neighbors, and independent of any other node in the graph given its neighbors.