Bayesian inference for models with intractable likelihoods, such as Markov random fields, poses a fundamental computational challenge due to the tradeoff between inferential accuracy and computational cost. Various MCMC methods have been developed to address this challenge. The exchange algorithm targets the exact posterior, but requires an expensive perfect sampling step at each iteration, which is often infeasible in practice. In contrast, path sampling approximates the Metropolis acceptance ratio using a precomputed grid of likelihood values, but may introduce bias when the grid is poorly chosen. We introduce a novel amortized MCMC framework that retains the theoretical validity of exact methods while substantially reducing the computational burden. The proposed approach employs a gradient-informed grid selection procedure and constructs a surrogate likelihood via Hermite interpolation, yielding a smooth approximation with low error. A simulation study characterizes the rate at which inferential accuracy improves as the number of grid points increases. We further demonstrate the practical performance of the method through applications to a hidden Potts model for satellite imagery and an autologistic model for Arctic ice floes.

翻译：对于似然函数难以处理的模型（如马尔可夫随机场），贝叶斯推断由于推断精度与计算开销之间的权衡而面临根本性计算挑战。为应对这一挑战，学界已发展出多种MCMC方法。交换算法虽能瞄准精确后验分布，但每次迭代需执行昂贵的完美采样步骤，实际中常不可行。相比之下，路径采样利用预计算的似然值网格近似Metropolis接受率，但网格选取不当可能引入偏差。本文提出一种新颖的摊销MCMC框架，在显著降低计算负担的同时保留精确方法的理论有效性。该方法采用基于梯度引导的网格选取过程，通过Hermite插值构建代理似然函数，获得低误差的光滑近似。仿真研究刻画了推断精度随网格点数量增加的提升速率。我们进一步通过卫星影像的隐式Potts模型与北极浮冰的自逻辑模型，展示了该方法在实际应用中的性能。