An introduction to thermodynamic integration and application to dynamic causal models

Area of Science:

• Neuroimaging analysis
• Computational neuroscience
• Statistical modeling

Background:

• Dynamic causal modeling (DCM) uses Bayesian model selection/averaging for neuroimaging data analysis.
• Current methods often approximate model evidence using variational Bayes, which has limitations.

Purpose of the Study:

• Introduce thermodynamic integration (TI) as an alternative for Bayesian model selection and averaging in DCM.
• Provide a theoretical understanding and practical guidance for applying TI in DCM.
• Address the computational demands of TI through efficient implementation.

Main Methods:

• Thermodynamic integration (TI) based on Markov chain Monte Carlo sampling.
• Explanation of theoretical foundations, including free energy and statistical physics origins.
• Practical application examples for user guidance.

Main Results:

• TI provides an asymptotically exact estimation of model evidence.
• Demonstrates successful application of TI in DCM, overcoming computational challenges.
• Highlights the availability of an efficient TI implementation in open-source software.

Conclusions:

• Thermodynamic integration is a viable and accurate method for Bayesian model selection and averaging in DCM.
• Efficient implementation and parallel processing can mitigate TI's computational cost.
• The presented TI implementation facilitates broader adoption in neuroimaging research.