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：具有难以计算的归一化函数的模型有许多应用。由于归一化常数是感兴趣参数的函数，因此标准的马尔可夫链蒙特卡罗算法不能用于这些模型的贝叶斯推断。已经开发了许多针对这些模型的算法。一些算法具有后验分布作为渐近分布的特性。其他不精确的渐近算法则没有这种性质。现有的关于使用这些算法评估近似值的指导有限。本文提出了两种新的诊断方法来解决这些问题。我们为提出的方法提供了理论上的保证，并在具有挑战性的例子中将其应用于几种算法。