Program - Brookhaven National Laboratory

[1] B. Paxton, L. Bildsten, A. Dotter et al., Astrophys. J. Suppl. Ser., 192:3 (2011). http://mesa.
sourceforge.net/. [2] F. Herwig, M. E. Bennet, S. Diehl et al., “Nucleosynthesis simulations for a wide
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Session LC Covariances
Wednesday March 6, 2013
Room: Empire East at 3:30 PM
LC 1 3:30 PM
On the Use of Zero Variance Penalty Conditions for the Generation of Covariance Matrix
Between Model Parameters
G. Noguere, P. Archier, C. De Saint Jean, B. Habert
CEA, DEN, DER, SPRC, Cadarache, F-13108 Saint-Paul-lez-Durance, France
Analytic and Monte-Carlo algorithms have been developed and implemented in the nuclear data code
CONRAD to generate covariances between model parameters. However, in the resolved resonance range
of the neutron cross sections, thousands model parameters and experimental data points are needed to
describe the main neutron reactions of interest for the nuclear applications. In practice, all of the model
parameter covariances cannot be simultaneously estimated from well-defined sets of experimental data.
The situation becomes more and more complex when the number of open reaction channels increases. This
optimization problem is nonconvex in general, making it difficult to find the global optima. A solution to
simplify the problem consists of dividing the model parameter sequence into blocks of variables, the uncertainties
of which can be propagated through fixed-order sequential data assimilation procedures. According
to definition and nomenclature used in statistics, we can identify the ”observable”, ”latent” and ”nuisance”
variables. Observable variables can be directly determined from the experimental data. Latent variables
(as opposed to observable variables) may define redundant parameters or hidden variables that cannot
be observed directly. This term reflects the fact that such variables are really there, but they cannot be
observed or measured for practical reasons. Nuisance variables (i.e. experimental corrections) correspond
to aspect of physical realities whose properties are not of particular interest as such but are fundamental
for assessing reliable model parameters. The methodology consists in calculating cross-covariance matrix
between Gaussian distributed parameters by introducing ”variance penalty” terms. This approach was
proposed by D.W. Muir for determining the contribution of individual correlated parameters to the uncertainty
of integral quantities. It provides a useful understanding of how the model parameters are related
to each other and ensures the positive-definiteness of the covariance matrix. Performances of the analytic
and Monte-Carlo models will be illustrated with covariances calculated between new Am-241 resonance
parameters recently established in the frame of the IRMM/CEA collaboration.
LC 2 4:00 PM
Evaluation of Uncertainties in βeff by Means of Deterministic and Monte Carlo Methods
I. Kodeli
Joˇzef Stefan Institute (JSI), Jamova 39, 1000 Ljubljana, Slovenia
173