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 to compute. We provide accurate approximations that make it possible to numerically calculate these quantities in the homogeneous case. Simulation studies indicate good performance when compared to Markov Chain Monte Carlo methods and at a tiny fraction of the time taken by those stochastic approaches. The value of our approximations 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：伊辛模型在统计建模及多领域推断中具有重要地位，但其归一化常数、活跃顶点平均数和自旋相互作用均值难以精确计算。本文针对同质情形提出精确近似方法，使得这些量的数值计算成为可能。仿真研究表明，与马尔可夫链蒙特卡洛方法相比，该方法在仅需其极短计算时间的情况下仍能保持良好性能。本文通过功能性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空间各向异性似然比检验，验证了近似方法的实用价值。