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Application of referenced thermodynamic integration to Bayesian model selection

Author

Listed:
  • Iwona Hawryluk
  • Swapnil Mishra
  • Seth Flaxman
  • Samir Bhatt
  • Thomas A Mellan

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.

Suggested Citation

  • Iwona Hawryluk & Swapnil Mishra & Seth Flaxman & Samir Bhatt & Thomas A Mellan, 2023. "Application of referenced thermodynamic integration to Bayesian model selection," PLOS ONE, Public Library of Science, vol. 18(8), pages 1-16, August.
    • Handle: RePEc:plo:pone00:0289889
    DOI: 10.1371/journal.pone.0289889
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