Discrete Markov random fields (MRFs) represent a class of undirected graphical models that capture complex conditional dependencies between discrete variables. Conducting exact posterior inference in these models is computationally challenging due to the intractable partition function, which depends on the model parameters and sums over all possible state configurations in the system. As a result, using the exact likelihood function is infeasible and existing methods, such as Double Metropolis-Hastings or pseudo-likelihood approximations, either scale poorly to large systems or underestimate the variability of the target posterior distribution. To address both computational burden and efficiency loss, we propose a new class of coordinate-rescaling sampling methods, which map the model parameters from the pseudo-likelihood space to the target posterior, preserving computational efficiency while improving posterior inference. Finally, in simulation studies, we compare the proposed method to existing approaches and illustrate that coordinate-rescaling sampling provides more accurate estimates of posterior variability, offering a scalable and robust solution for Bayesian inference in discrete MRFs.

翻译：离散马尔可夫随机场（MRFs）是一类无向图模型，用于刻画离散变量之间复杂的条件依赖关系。由于配分函数难以处理（其依赖于模型参数且需对系统中所有可能的状态构型求和），在这些模型中进行精确后验推断在计算上极具挑战性。因此，使用精确似然函数并不可行，而现有方法（如双重Metropolis-Hastings或伪似然近似）要么难以扩展至大规模系统，要么会低估目标后验分布的变异性。为同时解决计算负担与效率损失问题，我们提出了一类新的坐标重标度采样方法，该方法将模型参数从伪似然空间映射至目标后验空间，在保持计算效率的同时提升了后验推断的质量。最后，在模拟研究中，我们将所提方法与现有方法进行比较，结果表明坐标重标度采样能够更准确地估计后验变异性，为离散MRFs中的贝叶斯推断提供了一个可扩展且稳健的解决方案。