Fast approximations in the homogeneous Ising model for use in scene analysis

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 are intractable to compute. We provide accurate approximations that make it possible to numerically calculate these quantities in the homogeneous case. Simulation studies indicate good performance when compared to Markov Chain Monte Carlo methods and at a tiny fraction of the time taken by those stochastic approaches. The value of our approximations 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.