Approximations in the homogeneous Ising model
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2024-01-20
Authors
Murua-Sazo, Alejandro
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Abstract
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.
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This is a pre-print of the article Murua-Sazo, Alejandro, and Ranjan Maitra. "Approximations in the homogeneous Ising model." arXiv preprint arXiv:1712.02195 (2024).
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Sun Jan 01 00:00:00 UTC 2017