Bayesian Methods in Nuclear Physics

A workshop on Bayesian Methods in Nuclar Physics was held at the Institute for Nuclear Theory at the University of Washington in Seattle from June 13 to July 8, 2016. These pages continue the discussion initiated at this program. The workshop was the number 4 of the ISNET (Information and Statistics in Nuclear Experiments and Theory) family of meetings. Talks given at ISNET-3 and ISNET-5 are also listed here.

Goal: For statisticians and nuclear practitioners to jointly explore how Bayesian inference can enable progress on the frontiers of nuclear physics and open up new directions for the field.

References

Program paper repository (see organizers for username and password)

General Bayesian Statistics
Gaussian Process (GP) Models --- software and references
Hypothesis Testing and Model Comparison
Other Software

General Bayesian Statistics

Slides by Dave Higdon on Bayesian calibration of computer models.

The following are often recommended as introductory guides for physicists, because the examples and language are drawn from physics:

Data Analysis: A Bayesian Tutorial by Devinderjit Sivia and John Skilling. [Dick has a copy at the INT.]
Bayesian Logical Data Analysis for the Physical Sciences by Phil Gregory. [Dick has a copy at the INT.]
Bayes in the sky: Bayesian inference and model selection in cosmology by Roberto Trotta. Available from the arXiv or download the published version in Contemporary Physics 49, 71 (2008).
Testing a Point Null Hypothesis: The Irreconcilability of P Values and Evidence, Berger and Sellke (1987)

More advanced texts often recommended are:

Bayesian Data Analysis, by Andrew Gelman et al.

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Gaussian Process (GP) Models

GP software:

"Sample Size Calculations for Computer Experiments". Read the "About" tab first; it includes definitions of parameters used in the GP "correlation family" (which define the covariance). The "Sample Path Plots" tab has an app that lets you draw samples of functions that depend on user selected parameters (actually "hyperparameters") that specify the details of the correlation family.
Dan Foreman-Mackey Gaussian Process Python Library and Tutorial

GP references:

Efficient Global Optimization of Expensive Black-Box Functions by Donald Jones, Matthias Schonlau, and William Welch, Journal of Global Optimization 13: 455–492, 1998.
A Bayesian approach for parameter estimation and prediction using a computationally intensive model by Dave Higdon et al. [arXiv:1407.3017]
Gaussian Processes for Machine Learning, by Carl Edward Rasmussen and Christopher K. I. Williams. The full text is available (free!) as a pdf.
Fast Direct Methods for Gaussian Processes, by Sivaram Ambikasaran, Daniel Foreman-Mackey, Leslie Greengard, David W. Hogg, Michael O'Neil. [arXiv:1403.6015]

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Hypothesis Testing and Model Comparison

Testing hypotheses via a mixture estimation model, Kamary et al. (2014)
Philosophy and the practice of Bayesian statistics, Gelman and Shalizi (2012)
Bayesian evidence and predictivity of the inflationary paradigm, Gubitosi et al. (2016)
Bayes Factors, Kass and Raftery (1995)
Bayesian model selection and model averaging, Wasserman (2000)
Bayesian Model Averaging, Hoeting et al. (1999)

Other Software

A.W. Steiner: I have a generic C++ MCMC class as part of O₂scl which uses a traditional random walk, Metropolis-Hastings with a proposal distribution, or affine-invariant sampling. The basic header file is here and an example is here.

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Navigation

Questions for discussion

References

Participant information

Photos from the program

Statistics (Bayesian and other) humor

Workshop page at the INT

Organizers:
Nicolas Schunck (lead)
Dick Furnstahl
Dave Higdon
Andrew Steiner