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.

翻译：伊辛模型在许多应用的统计建模和推断中具有重要地位，但其归一化常数、活跃顶点的平均数量以及平均自旋相互作用（推断所需的量）在计算上难以处理。我们提供了精确的近似方法，使得在同质情况下能够数值计算这些量。模拟研究表明，我们的近似公式具有良好的性能，且不受马尔可夫随机场规模（节点数、图度数）的影响。通过功能磁共振成像激活检测实验中的贝叶斯推断，以及开心果树年产量增长空间模式各向异性的似然比检验，展示了我们近似公式的实际应用价值。