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.