Models with intractable normalising functions have numerous applications. Because the normalising constants are functions of the parameters of interest, standard Markov chain Monte Carlo cannot be used for Bayesian inference for these models. Many algorithms have been developed for such models. Some have the posterior distribution as the asymptotic distribution. Other ``asymptotically inexact'' algorithms do not possess this property. There is limited guidance for evaluating approximations based on these algorithms. We propose two new diagnostics that address these problems. We provide theoretical justification for our methods and apply them to several algorithms in the context of challenging examples.

翻译：具有不可归一化函数的模型在众多领域均有应用。由于归一化常数是待估参数的函数，标准马尔可夫链蒙特卡洛方法无法直接用于此类模型的贝叶斯推断。针对这类模型，目前已发展出多种算法。其中部分算法以后验分布作为渐近分布，而另一些"渐近非精确"算法则不具备这一性质。目前对基于这些算法的近似评估缺乏有效指导。我们提出两种新型诊断方法以解决上述问题。本文为所提方法提供了理论依据，并结合具有挑战性的实例将其应用于多种算法。