  The pseudo likelihood method of Besag(1974), has remained a popular method
for estimating Markov random field on a very large lattice, despite various
documented deficiencies. This is partly because it remains the only
computationally tractable method for large lattices. We introduce a novel
method to estimate Markov random fields defined on a regular lattice. The
method takes advantage of conditional independence structures and recursively
decomposes a large lattice into smaller sublattices. An approximation is made
at each decomposition. Doing so completely avoids the need to compute the
troublesome normalising constant. The computational complexity is $O(N)$, where
$N$ is the the number of pixels in lattice, making it computationally
attractive for very large lattices. We show through simulation, that the
proposed method performs well, even when compared to the methods using exact
likelihoods.
