Efficient use of Monte Carlo: the fast correlation coefficient

Random sampling methods are used for nuclear data (ND) uncertainty propagation, often in combination with the use of Monte Carlo codes (e.g., MCNP). One example is the Total Monte Carlo (TMC) method.
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Efficient use of Monte Carlo: the fast correlation coefficientEPJ Nuclear Sci. Technol. 4, 15 (2018) Nuclear Sciences© H. Sjöstrand et al., published by EDP Sciences, 2018 & Technologieshttps://doi.org/10.1051/epjn/2018019 Available online at: https://www.epj-n.org REGULAR ARTICLEEfficient use of Monte Carlo: the fast correlation coefficientHenrik Sjöstrand1,*, Nicola Asquith2, Petter Helgesson1,2, Dimitri Rochman3, and Steven van der Marck21 Department of Physics and Astronomy, Uppsala University, Uppsala, Sweden2 Nuclear Research and Consultancy Group NRG, Petten, The Netherlands3 Reactor Physics and Thermal Hydraulic Laboratory, Paul Scherrer Institut, Villigen, Switzerland Received: 16 January 2018 / Received in final form: 16 February 2018 / Accepted: 4 May 2018 Abstract. Random sampling methods are used for nuclear data (ND) uncertainty propagation, often in combination with the use of Monte Carlo codes (e.g., MCNP). One example is the Total Monte Carlo (TMC) method. The standard way to visualize and interpret ND covariances is by the use of the Pearson correlation coefficient, cov ðx; yÞ r¼ ; sx sy where x or y can be any parameter dependent on ND. The spread in the output, s, has both an ND component, s ND, and a statistical component, s stat. The contribution from s stat decreases the value of r, and hence it underestimates the impact of the correlation. One way to address this is to minimize s stat by using longer simulation run-times. Alternatively, as proposed here, a so-called fast correlation coefficient is used, cov ðx; yÞ cov ðxstat ; ystat Þ rfast ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi : s 2x s 2x;stat · s 2y s 2y;stat In many cases, cov ðxstat ; ystat Þ can be assumed to be zero. The paper explores three examples, a synthetic data study, correlations in the NRG High Flux Reactor spectrum, and the correlations between integral criticality experiments. It is concluded that the use of r underestimates the correlation. The impact of the use of rfast is quantified, and the implication of the results is discussed.1 Introduction output of these simulations can be interpreted in terms of the moments of the investigated output parameters, e.g.,Monte Carlo (MC) (or random sampling) methods are flux or keff. From the output from the large set of simulationfrequently used for nuclear data (ND) evaluation and with varying ND as input, the best estimate and theuncertainty propagation. For ND uncertainty propagation, uncertainty can be inferred. I.e., the MC method commonlyone frequently uses so-called random files, which is an MC used in ND uncertainty propagation is a standard randomrepresentation of the full PDF of the ND, i.e., the random sampling of input parameters. MC methods have thefiles implicitly contain both the best estimate of the ND and advantage that they propagate non-linear behavior. Inthe associated uncertainty. The random files can be addition, some methods, like the TMC method, can alsogenerated from the covariance matrix of the the ND propagate higher moments of input parameters, e.g.,library [1–3]. Alternatively, the Total Monte Carlo (TMC), skewness and kurtosis. Unfortunately, MC methods aremethod is used where the random files are generated computationally expensive, especially when combined withdirectly from the underlying physics ...