Mechanistic models of infectious disease spread are key to inferring spatiotemporal infectious disease transmission dynamics. Ideally, covariate data and the infection status of individuals over time would be used to parameterize such models. However, in reality, complete data are rarely available; for example, infection times are almost never observed. Bayesian data-augmented Markov chain Monte Carlo (MCMC) methods are commonly used to allow us to infer such missing or censored data. However, for large disease systems, these methods can be highly computationally expensive. In this paper, we propose two methods of approximate inference for such situations based on so-called emulation techniques. Here, both methods are set in a Bayesian MCMC framework but replace the computationally expensive likelihood function by a Gaussian process-based likelihood approximation. In the first method, we build an emulator of the discrepancy between summary statistics of simulated and observed epidemic data. In the second method, we develop an emulator of an importance sampling-based likelihood approximation. We show how both methods offer substantial computational efficiency gains over standard Bayesian MCMC-based method, and can be used to infer the transmission of complex infectious disease systems. We also show that importance sampling-based methods tend to perform more satisfactorily.

中文翻译：

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包含事件时间不确定性的空间传染病传播模型的基于仿真的推理

传染病传播的机制模型是推断时空传染病传播动态的关键。理想情况下，协变量数据和个人随时间的感染状态将用于参数化此类模型。然而，实际上，很少有完整的数据可用；例如，几乎从未观察到感染时间。贝叶斯数据增强马尔可夫链蒙特卡罗 (MCMC) 方法通常用于允许我们推断此类缺失或删失的数据。然而，对于大型疾病系统，这些方法在计算上可能非常昂贵。在本文中，我们基于所谓的仿真技术针对这种情况提出了两种近似推理方法。这里，这两种方法都设置在贝叶斯 MCMC 框架中，但用基于高斯过程的似然近似代替了计算量大的似然函数。在第一种方法中，我们构建了一个仿真器，用于模拟和观察到的流行病数据的汇总统计数据之间的差异。在第二种方法中，我们开发了一个基于重要性采样的似然近似的模拟器。我们展示了这两种方法如何比标准的基于贝叶斯 MCMC 的方法提供显着的计算效率增益，并且可用于推断复杂传染病系统的传播。我们还表明，基于重要性抽样的方法往往表现得更令人满意。我们开发了一个基于重要性采样的似然近似的模拟器。我们展示了这两种方法如何比标准的基于贝叶斯 MCMC 的方法提供显着的计算效率增益，并且可用于推断复杂传染病系统的传播。我们还表明，基于重要性抽样的方法往往表现得更令人满意。我们开发了一个基于重要性采样的似然近似的模拟器。我们展示了这两种方法如何比标准的基于贝叶斯 MCMC 的方法提供显着的计算效率增益，并且可用于推断复杂传染病系统的传播。我们还表明，基于重要性抽样的方法往往表现得更令人满意。