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On data assimilation with Monte-Carlo-calculated and statistically uncertain sensitivity coefficients

Andreas Pautz, Mathieu Hursin, Daniel Jerôme Siefman
2020
Journal paper
Abstract

Sensitivity coefficients from Monte Carlo neutron transport codes have uncertainties that can affect nuclear data adjustments with integral experiments. This paper presents an extended version of Generalized Linear Least Squares (GLLS), called xGLLS, that accounts for these uncertainties. With very large sensitivity uncertainties, xGLLS constrains the nuclear data adjustments so that the posterior biases and uncertainties are larger than with GLLS. However, for the range of sensitivity uncertainties realistically encountered, xGLLS does not produce adjustments different from GLLS. This indicates that sensitivity uncertainties are not important compared to experimental, modeling, methodological, and nuclear data uncertainties. To balance a simulation's accuracy with its computational cost, we recommend stopping a simulation once the uncertainty of a calculated integral parameter, caused by modeling and methodologies and by the sensitivities, is an order of magnitude smaller than that caused by nuclear data. (C) 2019 Elsevier Ltd. All rights reserved.

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Related concepts (33)
Sensitivity analysis
Sensitivity analysis is the study of how the uncertainty in the output of a mathematical model or system (numerical or otherwise) can be divided and allocated to different sources of uncertainty in its inputs. A related practice is uncertainty analysis, which has a greater focus on uncertainty quantification and propagation of uncertainty; ideally, uncertainty and sensitivity analysis should be run in tandem.
Monte Carlo method
Monte Carlo methods, or Monte Carlo experiments, are a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results. The underlying concept is to use randomness to solve problems that might be deterministic in principle. They are often used in physical and mathematical problems and are most useful when it is difficult or impossible to use other approaches. Monte Carlo methods are mainly used in three problem classes: optimization, numerical integration, and generating draws from a probability distribution.
Measurement uncertainty
In metrology, measurement uncertainty is the expression of the statistical dispersion of the values attributed to a measured quantity. All measurements are subject to uncertainty and a measurement result is complete only when it is accompanied by a statement of the associated uncertainty, such as the standard deviation. By international agreement, this uncertainty has a probabilistic basis and reflects incomplete knowledge of the quantity value. It is a non-negative parameter.
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