Overview

With the maturation of calculational methods such as lattice QCD for hadronic physics, ab initio and density functional theory approaches for nuclear structure and reactions (with applications to astrophysics and fundamental symmetries), and viscous hydrodynamic modeling of relativistic heavy-ion collisions, nuclear theory is entering an era of precision calculations. This is leading to increased demand for sophisticated uncertainty quantification, to effectively interface with, inform, and analyze experiments. The methods used to quantify errors are often based on frequentist statistical analysis, but Bayesian methods are becoming increasingly popular.

Bayesian statistics is a well-developed field, although it has not been part of the traditional education of nuclear theorists. In schematic form, Bayesian statistics treats the parameters or the model/theory as genuine random variables. It then uses Bayes theorem of probabilities to provide a recipe to compute their probability distribution (the “posterior”) in terms of prior information (e.g., about the data) and a likelihood function. For applications to fitting (“parameter estimation”), the posterior lets us infer, given the data we have measured, the most probable values of the parameters and predict values of observables with confidence intervals. Other applications involve deciding between alternative explanations or parameterizations (“model selection”). In practice, there are pitfalls in the implementation of this formalism and it is often a computationally hard problem.

Interest in Bayesian statistics has increased significantly in the past 10 years. The wide availability of large-scale computing resources has made the computation of the integrals needed for Bayesian inference easier. Modern experimental and observational facilities generate large amounts of data, often best analyzed and characterized through Bayesian methods. Bayesian methods are often preferred for under-constrained fits and inverse convolutions. In nuclear science, Bayesian methods have found their way into such areas as nuclear data, lattice QCD, dense matter, effective field theory, nuclear reactions, and parton distribution functions. These sub-fields have generally turned to Bayesian inference methods independently and in some cases without access to expert advice and guidance from professional statisticians.

Please submit your application by October 31, 2015.

Goals

This program will bring statisticians and nuclear practitioners together to explore how Bayesian inference can enable progress on the frontiers of nuclear physics and open up new directions for the field. Among the goals are to

• facilitate cross communication, fertilization, and collaboration on Bayesian applications among the nuclear sub-fields;
• provide the opportunity for nuclear physicists who are unfamiliar with Bayesian methods to start applying them to new problems;
• learn from the experts about innovative and advanced uses of Bayesian statistics, and best practices in applying them;
• learn about advanced computational tools and methods;
• critically examine the application of Bayesian methods to particular physics problems in the various subfields.

Program format

The program will include:

1. An environment where nuclear physicists of various stripes can compare and contrast the statistical tools they are using in order to maximize their benefit.
2. Talks on how Bayesian analysis is being used by research in fields related to nuclear physics: astrophysics, cosmology, and others.
3. Collaborative discussions with statisticians who can help guide our use of Bayesian inference.

Topics

Some of the themes/topics to be addressed are:

1. What do Bayesian techniques offer that frequentist statistics does not?
2. The influence of the prior and the various ways to minimize its impact, e.g. through Bayesian model checking.
3. The role of response functions, their advantages and pitfalls.
4. How to quantify systematic errors with Bayesian techniques.
5. Bayesian model calibration and Approximate Bayesian Computation (ABC).