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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. | Efficient use of Monte Carlo the fast correlation coefficient EPJ Nuclear Sci. Technol. 4 15 2018 Nuclear Sciences H. Sjöstrand et al. published by EDP Sciences 2018 amp Technologies https doi.org 10.1051 epjn 2018019 Available online at https www.epj-n.org REGULAR ARTICLE Efficient use of Monte Carlo the fast correlation coefficient Henrik Sjöstrand1 Nicola Asquith2 Petter Helgesson1 2 Dimitri Rochman3 and Steven van der Marck2 1 Department of Physics and Astronomy Uppsala University Uppsala Sweden 2 Nuclear Research and Consultancy Group NRG Petten The Netherlands 3 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 r 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 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 .