Presented at Los Alamos Neutron Scattering Center, Los Alamos, NM (July 25 - August 1, 2005)

Tutorials on Bayesian Methods in Nuclear Physics

Kenneth M. Hanson
T-16, Los Alamos National Laboratory


This set of tutorials provides an overview of Bayesian and probabilistic modeling, with special emphasis on cross-section evaluation. The fundamentals of the Bayesian approach are presented and illustrated with many examples. I will show how one can, with appropriate probabilistic modeling, cope with the usual goblins of data analysis, outliers, inconsistent data, and uncertainties in normalization. Systematic errors are easily handled. The technique of Markov chain Monte Carlo, which has revitalized Bayesian analysis, will be covered. Examples relevant to cross-section evaluation will help illustrate the basic ideas.

Tutorial 1 - Bayesian approach

probability - quantifies our degree of uncertainty
Bayes law and prior probabilities

Tutorial 2 - Bayesian modeling

Peelle's pertinent puzzle
Monte Carlo techniques; quasi-Monte Carlo
Bayesian update of cross sections using Jezebel criticality experiment

Tutorial 3 - Bayesian data analysis

linear fits to data with Bayesian interpretation
uncertainty in experimental measurements; systematic errors
treatment of outliers, discrepant data

Tutorial 4 - Bayesian calculations

Markov chain Monte Carlo technique
analysis of Rossi traces; alpha curve
background estimation in spectral data

Keywords: Bayesian analysis, nuclear physics, cross-section evaluation, priors, posterior, posterior sampling, experimental uncertainties, systematic uncertainty, disparate data, outliers, Peelle’s pertinent puzzle, Rossi trace, Markov chain Monte Carlo (MCMC), centroidal Voronoi tessellation (CVT), bibliography

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