MRC Centre for Global Infectious Disease Analysis, School of Public Health, Imperial College London, London, United Kingdom.
Saw Swee Hock School of Public Health and Institute of Data Science, National University of Singapore and National University Health System, Singapore, Singapore.
PLoS One. 2023 Aug 14;18(8):e0289889. doi: 10.1371/journal.pone.0289889. eCollection 2023.
Evaluating normalising constants is important across a range of topics in statistical learning, notably Bayesian model selection. However, in many realistic problems this involves the integration of analytically intractable, high-dimensional distributions, and therefore requires the use of stochastic methods such as thermodynamic integration (TI). In this paper we apply a simple but under-appreciated variation of the TI method, here referred to as referenced TI, which computes a single model's normalising constant in an efficient way by using a judiciously chosen reference density. The advantages of the approach and theoretical considerations are set out, along with pedagogical 1 and 2D examples. The approach is shown to be useful in practice when applied to a real problem -to perform model selection for a semi-mechanistic hierarchical Bayesian model of COVID-19 transmission in South Korea involving the integration of a 200D density.
评估归一化常数在统计学习的一系列主题中都很重要，特别是在贝叶斯模型选择中。然而，在许多实际问题中，这涉及到分析上难以处理的高维分布的积分，因此需要使用热力学积分（TI）等随机方法。在本文中，我们应用了 TI 方法的一个简单但被低估的变体，这里称为参考 TI，它通过使用明智选择的参考密度以有效的方式计算单个模型的归一化常数。本文阐述了该方法的优点和理论考虑，并提供了教学上的 1D 和 2D 示例。当将该方法应用于实际问题，即对涉及到 200D 密度积分的韩国 COVID-19 传播的半机械主义层次贝叶斯模型选择进行模型选择时，该方法在实践中被证明是有用的。
