Abstract
Hidden Markov random fields represent a complex hierarchical model, where the
hidden latent process is an undirected graphical structure. Performing inference for
such models is difficult primarily because the likelihood of the hidden states is often
unavailable. The main contribution of this article is to present approximate methods
to calculate the likelihood for large lattices based on exact methods for smaller lat-
tices. We introduce approximate likelihood methods by relaxing some of the dependen-
cies in the latent model, and also by extending tractable approximations to the likeli-
hood, the so-called pseudolikelihood approximations, for a large lattice partitioned into
smaller sublattices. Results are presented based on simulated data as well as inference
for the temporal-spatial structure of the interaction between up- and down-regulated
states within the mitochondrial chromosome of the Plasmodium falciparum organism.
Supplemental material for this article is available online.
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