Hidden Markov random field


In statistics, a hidden Markov random field is a generalization of a hidden Markov model. Instead of having an underlying Markov chain, hidden Markov random fields have an underlying Markov random field.
Suppose that we observe a random variable, where. Hidden Markov random fields assume that the probabilistic nature of is determined by the unobservable Markov random field,.
That is, given the neighbors of is independent of all other .
The main difference with a hidden Markov model is that neighborhood is not defined in 1 dimension but within a network, i.e. is allowed to have more than the two neighbors that it would have in a Markov chain. The model is formulated in such a way that given, are independent.
In the vast majority of the related literature, the number of possible latent states is considered a user-defined constant. However, ideas from nonparametric Bayesian statistics, which allow for data-driven inference of the number of states, have been also recently investigated with success, e.g.