*French CEA*,

Bruyeres-le-Chatel, France, July, 2006

## Improved predictive sampling using quasi-Monte Carlo with applications to neutron-cross-section evaluation

Kenneth M. Hanson

*Los Alamos National Laboratory*
### Abstract

The standard Monte Carlo (MC) technique is often used to estimate the integral of a function of many variables. When the cost of function evaluation is very high, however, as in the area of simulation science, it becomes important to look for more efficient techniques for numerical integration. The technique of quasi-Monte Carlo (QMC) offers improved error-convergence rates over MC. The heuristic reasoning behind selecting QMC point sets is that the points should be spread out as uniformly as possible, consistent with the desired point density. The Centroidal Voronoi Tessellation (CVT) algorithm achieves this goal even better than standard QMC algorithms. I demonstrate the usefulness of CVT in a problem in neutron-cross-section evaluation. The study involves combining directly measured neutron cross sections for 239Pu with about 1.5% standard error with a highly accurate criticality measurement (about 0.2%) to improve our knowledge of the cross sections. The relationship of the cross sections to the criticality measurement is obtained by a simulation, which is based on average cross sections for 30 neutron energy bins. After the Bayesian update, the goal is to propagate the uncertainties described by the posterior distribution into the uncertainties in the prediction of a new simulation. I show that the 30-dimensional quasi-random samples generated by CVT can improve the integration accuracy compared to standard MC for a criticality simulation.
Keywords: Monte Carlo integration, quasi-Monte Carlo, halftoning, repulsive particle model, Centroidal Voronoi Tessellation (CVT), high-dimensional point sets, covariance matrix, neutron fission cross sections, 239Pu, Bayesian analysis, posterior distribution, predictive distribution

**Keywords:** Monte Carlo integration, quasi-Monte Carlo, halftoning, repulsive particle model, Centroidal Voronoi Tessellation (CVT), high-dimensional point sets, covariance matrix, neutron fission cross sections, 239Pu, Bayesian analysis, posterior distribution, predictive distribution

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