Application of referenced thermodynamic integration to Bayesian model selection
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 stochasti...
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| Veröffentlicht in: | PloS one 2023-08, Vol.18 (8), p.e0289889-e0289889 |
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| creator | Hawryluk, Iwona Mishra, Swapnil Flaxman, Seth Bhatt, Samir Mellan, Thomas A |
| description | 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. |
| doi_str_mv | 10.1371/journal.pone.0289889 |
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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. 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This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.</rights><rights>COPYRIGHT 2023 Public Library of Science</rights><rights>2023 Hawryluk et al. This is an open access article distributed under the terms of the Creative Commons Attribution License: http://creativecommons.org/licenses/by/4.0/ (the “License”), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.</rights><rights>2023 Hawryluk et al 2023 Hawryluk et al</rights><rights>2023 Hawryluk et al. This is an open access article distributed under the terms of the Creative Commons Attribution License: http://creativecommons.org/licenses/by/4.0/ (the “License”), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. 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| 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 |
| title | Application of referenced thermodynamic integration to Bayesian model selection |
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