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
### Abstract

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

Viewgraphs for this presentation (pdf, 1980 KB)

Bibliography for this presentation (pdf, 20 KB)

Send e-mail to author at kmh@hansonhub.com

Return to Hanson presentations