2017/12/06 by Alejandro Murua, Murua-Sazo, Alejandro, Ranjan Maitra +1
Mathematics · #62E99 #62H10 #62H35 #68U10 #82B20 #Applications (stat.AP) #Computation (stat.CO) #FOS: Computer and information sciences #G.3 #I.4.8 #I.5 #Machine Learning (stat.ML) #Methodology (stat.ME) #Statistical Methods and Inference
paper · pdf · doi:10.48550/arxiv.1712.02195
openalex publication_date 2017/12/06 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28
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.