For many stochastic models of interest in systems biology, such as those describing biochemical reaction networks, exact quantification of parameter uncertainty through statistical inference is intractable. Likelihood-free computational inference techniques enable parameter inference when the likelihood function for the model is intractable but the generation of many sample paths is feasible through stochastic simulation of the forward problem. The most common likelihood-free method in systems biology is approximate Bayesian computation that accepts parameters that result in low discrepancy between stochastic simulations and measured data. However, it can be difficult to assess how the accuracy of the resulting inferences are affected by the choice of acceptance threshold and discrepancy function. The pseudo-marginal approach is an alternative likelihood-free inference method that utilises a Monte Carlo estimate of the likelihood function. This approach has several advantages, particularly in the context of noisy, partially observed, time-course data typical in biochemical reaction network studies. Specifically, the pseudo-marginal approach facilitates exact inference and uncertainty quantification, and may be efficiently combined with particle filters for low variance, high-accuracy likelihood estimation. In this review, we provide a practical introduction to the pseudo-marginal approach using inference for biochemical reaction networks as a series of case studies. Implementations of key algorithms and examples are provided using the Julia programming language; a high performance, open source programming language for scientific computing (https://github.com/davidwarne/Warne2019_GuideToPseudoMarginal).

中文翻译：

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用于系统生物学计算推理的伪边际方法实用指南。

对于系统生物学中感兴趣的许多随机模型，例如那些描述生化反应网络的随机模型，通过统计推断精确量化参数不确定性是难以处理的。当模型的似然函数难以处理但通过前向问题的随机模拟生成许多样本路径是可行的时，无似然计算推理技术可以实现参数推理。系统生物学中最常见的无似然方法是近似贝叶斯计算，它接受导致随机模拟和测量数据之间差异较小的参数。但是，可能很难评估接受阈值和差异函数的选择对结果推断的准确性有何影响。伪边际方法是一种替代的无似然推理方法，它利用似然函数的蒙特卡罗估计。这种方法有几个优点，特别是在生化反应网络研究中典型的嘈杂、部分观察的时间过程数据的背景下。具体而言，伪边际方法有助于精确推理和不确定性量化，并且可以有效地与粒子滤波器结合以实现低方差、高精度似然估计。在这篇综述中，我们通过一系列案例研究对使用生化反应网络推理的伪边际方法进行了实用介绍。使用 Julia 编程语言提供了关键算法和示例的实现；高性能，