Approximations in the homogeneous Ising model
This provides practical computational tools for statistical inference in applications like neuroscience and agriculture, though it appears incremental as it focuses on approximations for an existing model.
The authors tackled the computational intractability of key quantities in the homogeneous Ising model by providing accurate approximations for the normalizing constant, mean number of active vertices, and mean spin interaction. Simulation studies showed good performance that scales with graph size, and the approximations were applied to Bayesian inference in fMRI activation detection and likelihood ratio testing for anisotropy in pistachio tree yield patterns.
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.