Abstract Doubly intractable distributions arise in many settings, for example, in Markov models for point processes and exponential random graph models for networks. Bayesian inference for these models is challenging because they involve intractable normalizing “constants” that are actually functions of the parameters of interest. Although several computational methods have been developed for these models, each can be computationally burdensome or even infeasible for many problems. We propose a novel algorithm that provides computational gains over existing methods by replacing Monte Carlo approximations to the normalizing function with a Gaussian process-based approximation. We provide theoretical justification for this method. We also develop a closely related algorithm that is applicable more broadly to any likelihood function that is expensive to evaluate. We illustrate the application of our methods to challenging simulated and real data examples, including an exponential random graph model, a Markov point process, and a model for infectious disease dynamics. The algorithm shows significant gains in computational efficiency over existing methods, and has the potential for greater gains for more challenging problems. For a random graph model example, we show how this gain in efficiency allows us to carry out accurate Bayesian inference when other algorithms are computationally impractical. Supplementary materials for this article are available online.

中文翻译：

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双重难处理分布的函数仿真方法

摘要 双重难以处理的分布出现在许多环境中，例如，在点过程的马尔可夫模型和网络的指数随机图模型中。这些模型的贝叶斯推理具有挑战性，因为它们涉及难以处理的归一化“常数”，这些“常数”实际上是感兴趣参数的函数。尽管已经为这些模型开发了几种计算方法，但对于许多问题，每种方法在计算上都很繁重，甚至不可行。我们提出了一种新算法，该算法通过用基于高斯过程的近似替换归一化函数的蒙特卡罗近似来提供优于现有方法的计算增益。我们为这种方法提供了理论依据。我们还开发了一种密切相关的算法，该算法更广泛地适用于任何评估成本高的似然函数。我们说明了我们的方法在具有挑战性的模拟和真实数据示例中的应用，包括指数随机图模型、马尔可夫点过程和传染病动力学模型。与现有方法相比，该算法显示出计算效率的显着提高，并且有可能为更具挑战性的问题带来更大的收益。对于随机图模型示例，我们展示了当其他算法在计算上不切实际时，这种效率的提高如何使我们能够执行准确的贝叶斯推理。本文的补充材料可在线获取。包括指数随机图模型、马尔可夫点过程和传染病动力学模型。与现有方法相比，该算法显示出计算效率的显着提高，并且有可能为更具挑战性的问题带来更大的收益。对于随机图模型示例，我们展示了当其他算法在计算上不切实际时，这种效率的提高如何使我们能够执行准确的贝叶斯推理。本文的补充材料可在线获取。包括指数随机图模型、马尔可夫点过程和传染病动力学模型。与现有方法相比，该算法显示出计算效率的显着提高，并且有可能为更具挑战性的问题带来更大的收益。对于随机图模型示例，我们展示了当其他算法在计算上不切实际时，这种效率的提高如何使我们能够执行准确的贝叶斯推理。本文的补充材料可在线获取。我们展示了当其他算法在计算上不切实际时，这种效率的提高如何使我们能够进行准确的贝叶斯推理。本文的补充材料可在线获取。我们展示了当其他算法在计算上不切实际时，这种效率的提高如何使我们能够进行准确的贝叶斯推理。本文的补充材料可在线获取。