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. The standard way to visualize and interpret ND covariances is by the use of the Pearson correlation coefficient, rho = cov(x, y)/sigma(x) x sigma(y), where x or y can be any parameter dependent on ND. The spread in the output, sigma, has both an ND component, sigma(ND), and a statistical component, sigma(stat). The contribution from sigma(stat) decreases the value of rho, and hence it underestimates the impact of the correlation. One way to address this is to minimize sigma(stat) by using longer simulation run-times. Alternatively, as proposed here, a so-called fast correlation coefficient is used, rho(fast) = cov (x, y)-cov (x(stat), y(stat))/root sigma(2)(x)-sigma(2)(x,stat).root sigma(2)(y)-sigma(2)(y,stat) . In many cases, cov (x(stat), y(stat)) 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 rho underestimates the correlation. The impact of the use of rho(fast) is quantified, and the implication of the results is discussed