Relaxometry models compared with Bayesian techniques: ganglioside micelle example

Area of Science:

• Physical Chemistry
• Computational Chemistry
• Biophysics

Background:

• Nuclear Magnetic Relaxation Dispersion (NMRD) probes slow dynamics in complex liquids like micelle systems.
• Accurate theoretical NMRD models are crucial for understanding systems such as ionic liquids and electrolytes.
• Comparing different NMRD models is essential for advancing scientific understanding beyond physico-chemical considerations.

Purpose of the Study:

• To develop and exemplify a methodology for Bayesian model comparison in NMRD data analysis.
• To determine the optimal number of water pools within a ganglioside micelle system using Bayesian evidence.
• To introduce and define Ockham-entropy for explaining model comparison outcomes.

Main Methods:

• Bayesian model comparison was performed by computing Bayesian evidence.
• The thermodynamic integral was solved using Markov chain Monte Carlo (MCMC) simulations.
• Model performance was assessed by comparing Bayesian evidence against mean squared deviation (χ2).

Main Results:

• The analysis concluded that a two-water-pool model best describes the ganglioside micelle system based on Bayesian evidence.
• Models with one or three water pools were statistically ruled out by the Bayesian evidence.
• While a three-pool model yielded a better fit (lower χ2), Bayesian evidence correctly identified the more parsimonious two-pool model.

Conclusions:

• Bayesian evidence is superior to simple fit quality metrics (like χ2) for ranking NMRD model uncertainty.
• Approximate criteria like Akaike and Bayesian Information Criteria may yield incorrect model selections compared to full Bayesian integration.
• The developed Bayesian methodology is general and applicable to model development across various scientific research areas.