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: ρ = cov(x,y)/σ_x*σ_y, where x or y can be any parameter dependent on ND. The spread in the output, σ, has both an ND component, σ_ND, and a statistical component, σ_stat. The contribution from σ_stat decreases the value of ρ, and hence it underestimates the impact of the correlation. One way to address this is to minimize σ_stat by using longer simulation run-times. Alternatively, as proposed here, a so-called fast correlation coefficient is used: ρ_fast = [cov(x,y) - cov(x_stat,y_stat)]/[√(σ_x² - σ_xstat²)*√(σ_y²-σ_ystat²)]. In many cases, cov(x_stat,y_stat) can be assumed to be zero. The paper explores 3 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 ρ underestimates the correlation. The impact of the use of ρ_fast is quantified, and the implication of the results is discussed. (authors)