Inference for doubly intractable distributions is challenging because the intractable normalizing functions of these models include parameters of interest. Previous auxiliary variable MCMC algorithms are infeasible for multi-dimensional models with large data sets because they depend on expensive auxiliary variable simulation. We develop a fast Bayesian indirect algorithm by replacing an expensive auxiliary variable simulation from a probability model with a computationally cheap simulation from a surrogate model. We learn the relationship between the surrogate model parameters and the probability model parameters using Gaussian process approximations. We apply our methods to challenging examples, and illustrate that the algorithm addresses both computational and inferential challenges for doubly intractable distributions. Especially for a large social network model with 10 parameters, we show that our method can reduce computing time from about 2 weeks to 5 hours, compared to the previous method.

中文翻译：

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具有难以处理的归一化函数的模型的贝叶斯间接推理

对双重难以处理的分布的推断具有挑战性，因为这些模型的难以处理的归一化函数包括感兴趣的参数。以前的辅助变量 MCMC 算法对于具有大数据集的多维模型是不可行的，因为它们依赖于昂贵的辅助变量模拟。我们通过用来自代理模型的计算成本低的模拟替换来自概率模型的昂贵的辅助变量模拟来开发一种快速贝叶斯间接算法。我们使用高斯过程近似来学习代理模型参数和概率模型参数之间的关系。我们将我们的方法应用于具有挑战性的示例，并说明该算法解决了双重难以处理的分布的计算和推理挑战。