Training in Advanced Low-Energy Nuclear Theory
Course 11. Learning from Data: Bayesian Methods and Machine Learning
University of York, UK, June 10-28, 2019
Introduction
In recent years there has been an explosion of interest in the use of Bayesian methods in nuclear physics. These methods are being used to quantify the uncertainties in theoretical work on topics ranging from the NN force to high-energy heavy-ion collisions, develop more reliable extrapolants of nuclear-energy-density functionals towards the dripline, predict the impact that future NICER observations may have on the equation of state of neutron matter, and determine whether or not nucleon resonances are present in experimental data. Meanwhile machine learning is gaining increased currency as a method for identifying interesting signals in both experiments and simulations. While most nuclear-physics Ph.D. students are taught some standard (frequentist) statistics as part of their graduate course work, very few encounter Bayesian methods until they are engaged in research. But Bayesian methods provide a coherent and compelling framework to think about inference, and so can be applied to many important questions in nuclear physics. The overall learning goal of this school is to take students who have had no previous exposure to Bayes’ theorem and show them how it can be applied to problems of parameter estimation, model selection, and machine learning.
Learning outcomes
Upon completion of this course students should be able to:
- Apply the rules of probability to derive posterior probability distributions for simple problems involving prior information on parameters and various standard likelihood functions.
- Perform Bayesian parameter estimation, including in cases where marginalization over nuisance parameters is required.
- Use Monte Carlo sampling to generate posterior probability distributions and identify problems were standard sampling is likely to fail.
- Compute an evidence ratio and explain what it means.
- Explain machine learning from a Bayesian perspective and employ a testing and training data set to develop and validate a Gaussian-process model.
- Employ these methods in the context of specific nuclear-physics problems.
- Be able to understand, appreciate, and criticize the growing literature on Bayesian statistics and machine learning for low-energy nuclear physics applications.
Preparation
Please follow the instructions at the installation page.
Course contents
Course material is available at the following public github repository https://github.com/NuclearTalent/Bayes2019
This repository will be updated to correct for typos and to provide more explanations when needed. The end-of-school commit is tagged v1.0.
The following topics will be covered:
- Basics of Bayesian statistics
- Bayesian parameter estimation
- Why Bayes is better
- MCMC sampling
- Assigning probabilities
- Model selection
- Special topic: Application of Bayesian methods in nuclear physics
- Gaussian processes
- Model checking
- Special topic: Bayesian methods and machine learning
Schedule of the lecture weeks:
The material of the exercise groups can be found here.
Jupyter notebooks will be used extensively throughout the course. Some notebooks introducing notebooks can be found here.
Mini-projects
Go to the mini-projects.
Discussion questions
Questions on Bayesian statistics and its application to nuclear physics problems are collected in this FAQ page. Participants are strongly encouraged to try these questions and propose answers, and also to suggest new questions to be added.
Teachers and local organization
Lecturers:
- Christian Forssén, Chalmers University of Technology, Sweden
- Dick Furnstahl, Ohio State University, USA
- Daniel Phillips, Ohio University, USA; TU Darmstadt and EMMI, Germany
Teaching facilitators
- John Bower, NSCL, Michigan State University, USA
- Christian Drischler, University of California, Berkeley, USA
Local organizer
- Alessandro Pastore, University of York, UK
This TALENT school is made possible with generous funding from the Science and Technology Facilities Council STFC in the UK.
Daily schedule
There are two lectures every morning. Each lecture is approximately 2x40 min with a small break in the middle. There is a longer coffee break between the two morning lectures. The afternoons will be devoted to exercise sessions in the computer lab with extra support from the two facilitators. Students will work on a mix of discussion questions, computer exercises and mini projects. Every day ends with a wrap-up discussion session. We also will have a poster session with discussion at the end of the second week.
The organization of a typical course day is as follows:
| Time | Activity |
|---|---|
| 9.00 - 10.30 | Lecture 1 |
| 10.30 - 11.00 | Coffee break |
| 11.00 - 12.30 | Lecture 2 |
| 12.30 - 14.00 | Lunch |
| 14.00 - 16.30 | Exercise session with afternoon tea break |
| 16.30 - 17.30 | Wrap-up |
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