  The Ising model is important in statistical modeling and inference in many
applications, however its normalizing constant, mean number of active vertices
and mean spin interaction -- quantities needed in inference -- are
computationally intractable. We provide accurate approximations that make it
possible to numerically calculate these quantities in the homogeneous case.
Simulation studies indicate good performance of our approximation formulae that
are scalable and unfazed by the size (number of nodes, degree of graph) of the
Markov Random Field. The practical import of our approximation formulae is
illustrated in performing Bayesian inference in a functional Magnetic Resonance
Imaging activation detection experiment, and also in likelihood ratio testing
for anisotropy in the spatial patterns of yearly increases in pistachio tree
yields.

Methodology;Applications;Computation;Machine Learning