Application of referenced thermodynamic integration to Bayesian model selection

Iwona Hawryluk, Swapnil Mishra, Seth Flaxman, Samir Bhatt and Thomas A Mellan

PLOS ONE, 2023, vol. 18, issue 8, 1-16

Abstract: 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.

Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:plo:pone00:0289889

DOI: 10.1371/journal.pone.0289889

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