Fast spatial inference in the homogeneous Ising model

Date
2017-01-01
Authors
Murua, Alejandro
Maitra, Ranjan
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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 are intractable. We provide accurate approximations that make it possible to calculate these quantities numerically. Simulation studies indicate good performance when compared to Markov Chain Monte Carlo methods and at a tiny fraction of the time. The methodology is also used to perform Bayesian inference in a functional Magnetic Resonance Imaging activation detection experiment.

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<p>This is a pre-print of the article Murua, Alejandro, and Ranjan Maitra. "Fast spatial inference in the homogeneous Ising model." <em>arXiv preprint arXiv:1712.02195</em> (2017). Posted with permission.</p>
Keywords
finger-tapping, fMRI, hypergeometric distribution, path sampling, Swendsen-Wang algorithm, Stirling’s approximation, Wang-Landau algorithm
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