Model selection is a fundamental part of the applied Bayesian statistical methodology. Metrics such as the Akaike Information Criterion are commonly used in practice to select models but do not incorporate the uncertainty of the models' parameters and can give misleading choices. One approach that uses the full posterior distribution is to compute the ratio of two models' normalising constants, known as the Bayes factor. Often in 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 variation of the TI method, 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 explicit pedagogical 1 and 2D examples. Benchmarking is presented with comparable methods and we find favourable convergence performance. 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.

翻译：模型选择是应用的巴伊西亚统计方法的一个基本部分。诸如Akaike信息标准等计量方法在实践中通常用于选择模型,但并不包含模型参数的不确定性,而且可以作出误导性的选择。一种使用完整后部分布的方法是计算两个模型的常数(称为拜亚系数)的正常化常数(称为拜亚系数)的比率。通常在现实情况下,这涉及综合分析难以分析的高维分布,因此需要使用热力集成(TI)等随机方法。在本文中,我们采用称为参考TI的TI方法的变异方法,该方法通过使用明智选择的参考密度,以有效的方式计算单一模型的常数。该方法和理论考虑的优点与明确的教学1和2D实例一起列出。基准采用类似的方法,我们发现良好的趋同性表现。在实际应用该方法时,在实际应用一个问题时,该方法很有用处――对一个半机械级的Bayesian模型进行模型选择,该模型使用明智的参考密度为韩国的COVID-19传输密度一体化。