Ohio State University
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INT Program INT-16-2a|
Bayesian Methods in Nuclear Physics
June 13 - July 8, 2016
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.
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.
The program will include:
We will follow the standard format of daily talks on particular applications of
Bayesian methods by the participants, supplemented by informal afternoon meetings.
In addition, we will have regular overview lectures/tutorials by the experts on Bayesian
inference and computational methods. We seek to mix the communities and address
common features within the context of specific problems (which will have many
overlaps). However, the general organization would be by themes relevant to the
Bayesian techniques themselves, since it is the common thread of the various
communities we want to involve.
- An environment where nuclear physicists of various stripes can compare and
contrast the statistical tools they are using in order to maximize their benefit.
- Talks on how Bayesian analysis is being used by research in fields related to
nuclear physics: astrophysics, cosmology, and others.
- Collaborative discussions with statisticians who can help guide our use of Bayesian
Some of the themes/topics to be addressed are:
- What do Bayesian techniques offer that frequentist statistics does not?
- The influence of the prior and the various ways to minimize its impact, e.g.
through Bayesian model checking.
- The role of response functions, their advantages and pitfalls.
- How to quantify systematic errors with Bayesian techniques.
- Bayesian model calibration and Approximate Bayesian Computation (ABC).