Lepricon, Combination of Correlated Data and Peelle's Puzzle

Abstract

The purpose of this discourse is elaboration of the least-squares formalism for averaging any number of correlated data. A procedure is considered, in a rather general formulation, which serves to determine m parameters by n correlated experimental data on possibly different functions of the parameters. If m > n, the very same procedure applies to the adjustment of a given library of m correlated parameters by a set of n relevant correlated data which might even be correlated to the given parameters. However, casual or indifferent application of the procedure might yield erroneous or even meaningless results. A very simple, and relevant, example is the combination of averages over partially overlapping sets of data. The combination yields a result which is different from the true average of the data, i.e. the average over the union of partial data sets. Further, when the measured quantities are nonlinear functions of the parameters, special care should be taken in order not to exceed the range of validity of the conventional, i.e. linearized, algorithm. One should also consider the mutual consistency of the given data, for even few outliers, which in a limited data set are highly improbable, might severely bias the resulting estimates of the unknown parameters. We discuss several observations and offer some comments on the applicability of the least-squares combination of correlated data.

Neutronics experiments for uncertainty assessment of tritium breeding in HCPB and HCLL blanket mock-ups irradiated with 14 MeV neutrons

“…For the calculation of uncertainties in the TPR due to uncertainties of the underlying nuclear data common sets of covariance data were used for both methodological approaches. The covariance data were taken mainly from JEFF3.2β, NDF/B-VI.8, /B-VII, IRDF-02 and the ZZ SCALE6.0/COVA-44G libraries 5 and COMMARA-2.0 [22] neutron cross-section covariance libraries. Total uncertainties in the TPR calculated using the SUSD3D code and based on various covariance matrix evaluations are given in tables 3 and 4.…”

“…To this end, the EU is conducting a dedicated neutronics R&D program that includes the development of computational tools, the generation of high-quality nuclear data and their validation by means of integral experiments and, later, neutronics experiments in TBMs in ITER [3]. Within the framework of this program, and integrated into the Joint European Fission Fusion File project (JEFF) [4], neutron crosssection and covariance data libraries are developed, as well as computational tools comprising sensitivity and uncertainty codes based on Monte Carlo and deterministic approaches (MCSEN [5], SUSD3D [6]).…”

Neutronics R&D efforts in support of the European breeder blanket development programme

“…The Monte Carlo based calculation of uncertainties of nuclear responses in the TBM in ITER requires in addition the capability to calculate sensitivities for responses by the track length estimator. Suitable algorithms based on the differential operator method were developed to this end and implemented in a local version of the Monte Carlo code MCNP, called MCSEN [21]. This approach enables the efficient calculation of sensitivities for neutron fluxes and nuclear responses such as reaction rates in a geometry cell of an arbitrary threedimensional configuration.…”

Confluence of calculational and experimental information for determination of power distribution and burnup

“…In systems with limited knowledge the Gaussian distribution has proven to be the best choice for data inference for both systematic and statistical uncertainties (Janes, 1983). The statistical uncertainties rk and ri are described by zero means and covariance matrices (rkr~, where T denotes transpose and k, i = 1 ..... K. For systems with limited knowledge about the magnitudes of the biases, it is suggested (Perel et al, 1994) that we describe the systematic uncertainty by a Gaussian with zero mean and either diagonal (bkb~ (if k equals 0 or zero (if k does not equal 0 covariance matrix, rather than by a rectangular probability distribution. This limited knowledge should be utilized to evaluate variances and not means of the biases, which are in this case assumed to be zero.…”

“…The formulas for the general multi-source, multi-variate statistical confluence of the correlated information are derived and presented in the following section. In contrast to the intuitive and intricate derivation of the general adjustment prescriptions given by Perel et al (1994), we exploit the Bayesian statistics, taking advantage of its fundamental significance for any type of data adjustment or evaluation, confirmed again by Frthner (1994). The downto-earth problem is how to estimate the prior knowledge required for the confluence, namely statistical properties of the uncertainties (both statistical and systematic).…”