* Bayesian Inference and Maximum Entropy Methods in Science and Engineering*,

K. H. Knuth, A. E. Abbas, R. D. Morris, and J. P. Castle, eds.,

*AIP Conf. Proc.* **803**, pp. 431-439 (AIP, Melville, 2005)

## Bayesian analysis of inconsistent measurements of neutron cross sections

Kenneth M. Hanson

*Los Alamos National Laboratory*
### Abstract

The evaluation of neutron cross sections as a function of energy is fraught with inconsistent measurements. I describe a Bayesian approach to deal with the inconsistencies by probabilistically modeling the possibility of discrepant data and data sets with long-tailed likelihood functions. Systematic normalization uncertainties in each data set are included by considering the normalization to be a variable with specified uncertainty. By characterizing its uncertainty with a mixture of Cauchy and Gaussian distributions, data sets that disagree with the majority of others are given less weight in terms of normalization, but still provide useful information about the energy dependency of the cross sections. I demonstrate the approach with data sets of neutron fission cross sections for americium 243. Samples from the posterior obtained with the Markov Chain Monte Carlo technique are used to estimate the posterior mean and standard error.

**Keywords:** neutron fission cross sections, americium-243, Bayesian analysis, normalization uncertainty, discrepant data, outliers, long-tailed likelihood, Cauchy distribution, Student t-distribution

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