A large class of spatial models contains intractable normalizing functions, such as spatial lattice models, interaction spatial point processes, and social network models. Bayesian inference for such models is challenging since the resulting posterior distribution is doubly intractable. Although auxiliary variable MCMC (AVM) algorithms are known to be the most practical, they are computationally expensive due to the repeated auxiliary variable simulations. To address this, we propose delayed-acceptance AVM (DA-AVM) methods, which can reduce the number of auxiliary variable simulations. The first stage of the kernel uses a cheap surrogate to decide whether to accept or reject the proposed parameter value. The second stage guarantees detailed balance with respect to the posterior. The auxiliary variable simulation is performed only on the parameters accepted in the first stage. We construct various surrogates specifically tailored for doubly intractable problems, including subsampling strategy, Gaussian process emulation, and frequentist estimator-based approximation. We validate our method through simulated and real data applications, demonstrating its practicality for complex spatial models.

翻译：一大类空间模型包含难处理的归一化函数，例如空间格点模型、交互空间点过程以及社交网络模型。此类模型的贝叶斯推断具有挑战性，因为由此产生的后验分布是双重难处理的。尽管已知辅助变量MCMC（AVM）算法是最实用的方法，但由于需要重复模拟辅助变量，其计算成本高昂。为解决此问题，我们提出了延迟接受AVM（DA-AVM）方法，该方法可以减少辅助变量模拟的次数。该核函数的第一阶段使用一个廉价的代理模型来决定是接受还是拒绝所提出的参数值。第二阶段则保证了关于后验分布的细致平衡。辅助变量模拟仅对在第一阶段被接受的参数执行。我们构建了多种专门针对双重难处理问题定制的代理模型，包括子采样策略、高斯过程仿真以及基于频率派估计量的近似方法。我们通过模拟数据和实际数据应用验证了我们的方法，证明了其对于复杂空间模型的实用性。