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Related Concept Videos

Thermodynamic Systems01:06

Thermodynamic Systems

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A thermodynamic system is a set of objects whose thermodynamic properties are of interest. The system is considered to be embedded in its surroundings or the environment. The system and its environment can exchange heat and do work on each other through a boundary that separates them. However, the immediate surroundings of the system interact with it directly and therefore have a much stronger influence on its behavior and properties.
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Thermodynamic potentials are state functions that are extremely useful in analyzing a thermodynamic system. They have dimensions of energy. The four important thermodynamic potentials are internal energy, enthalpy, Helmholtz free energy, and Gibbs free energy. These thermodynamic potentials can be expressed using two of the following variables: pressure, volume, temperature, and entropy. These two variables are expressed as the rate of change of the thermodynamic potential with respect to other...
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Application of referenced thermodynamic integration to Bayesian model selection.

Iwona Hawryluk1, Swapnil Mishra2, Seth Flaxman3

  • 1MRC Centre for Global Infectious Disease Analysis, School of Public Health, Imperial College London, London, United Kingdom.

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|August 14, 2023
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Summary

Referenced thermodynamic integration (TI) efficiently calculates normalising constants for complex models. This method aids Bayesian model selection, even for high-dimensional problems like COVID-19 transmission analysis.

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Area of Science:

  • Statistical Learning
  • Bayesian Inference
  • Computational Statistics

Background:

  • Evaluating normalising constants is crucial for Bayesian model selection.
  • High-dimensional and analytically intractable distributions pose significant computational challenges.
  • Stochastic methods like thermodynamic integration (TI) are often required.

Purpose of the Study:

  • To introduce and evaluate a variation of TI called referenced TI.
  • To demonstrate the efficiency of referenced TI in computing normalising constants.
  • To apply referenced TI to a practical problem in Bayesian model selection.

Main Methods:

  • Utilisation of a referenced thermodynamic integration (TI) approach.
  • Employing a reference density to simplify the integration process.
  • Application to a semi-mechanistic hierarchical Bayesian model for COVID-19 transmission.

Main Results:

  • Referenced TI efficiently computes normalising constants for high-dimensional distributions.
  • The method proved effective in a 200D integration scenario for COVID-19 modeling.
  • Pedagogical examples in 1D and 2D illustrate the approach's advantages.

Conclusions:

  • Referenced TI offers an efficient and practical solution for calculating normalising constants.
  • This method enhances Bayesian model selection capabilities for complex, real-world problems.
  • The approach is particularly valuable for high-dimensional Bayesian models.