Application of referenced thermodynamic integration to Bayesian model selection

• Published in: PloS one Vol. 18; no. 8; p. e0289889
• Main Authors: Hawryluk, Iwona, Mishra, Swapnil, Flaxman, Seth, Bhatt, Samir, Mellan, Thomas A
• Format: Journal Article
• Language: English
• Published: United States Public Library of Science 14.08.2023; Public Library of Science (PLoS)
• Subjects: Bayes Theorem; Bayesian analysis; Bayesian information criterion; COVID-19; Density; Dimensional analysis; Humans; Hypotheses; Integrals; Integration; Machine learning; Mathematical models; Medicine and Health Sciences; Methods; Modelling; People and places; Physical Sciences; Republic of Korea; Research and analysis methods; Stochastic methods; Stochasticity; Thermodynamics; Republic of Korea; South Korea
• ISSN: 1932-6203; 1932-6203
• DOI: 10.1371/journal.pone.0289889

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.