Schematic illustration of the density of the Dirichlet distribution for true model mixing.
Schematic illustration of the density of the Dirichlet distribution for true model mixing.
Image courtesy of V. Kejzlar

The Science

Physicists use theoretical models to study physical quantities, such as the mass of nuclei, where they do not have experimental data. However, using a single imperfect theoretical model can lead to misleading results. To improve the quality of extrapolated predictions, scientists can instead use several different models and mix their results. In this way, scientists make the most of the collective wisdom of multiple models and obtain the best prediction from the most current experimental information.

The Impact

To improve the predictability of complex computational models, a team of nuclear physicists and statisticians proposed a novel statistical method. This method uses a statistical process called Bayes' theorem to revise the probability of a hypothesis as new data are obtained. The resulting machine learning framework uses the so-called Dirichlet distribution. This statistical process combines the results of several imperfect models. The researchers demonstrated the ability of the proposed mixing techniques to mine data on nuclear masses. 

Summary

This research demonstrated that global and local mixtures of models have excellent performance in both the accuracy of their predictions and their uncertainty quantification. These mixtures appear to be preferable to classical Bayesian model averaging, the conventional approach. Additionally, the researchers’ analysis indicates that improving model predictions through straightforward mixing leads to more robust extrapolations than does mixing of corrected models. 

Contact

Witold Nazarewicz
Facility for Rare Isotope Beams/Michigan State University
witek@frib.msu.edu

Funding

This material is based on work supported by the Department of Energy Office of Science, Office of Nuclear Physics.

Publications

Vojtech Kejzlar, V., Neufcourt, V., and Nazarewicz, W., Local Bayesian Dirichlet mixing of imperfect models. Scientific Reports 13, 19600 (2023). [DOI: 10.1038/s41598-023-46568-0]