Efficient estimation of unfactorizable systematic uncertainties

Abstract Accurate assessment of systematic uncertainties is an increasingly vital task in physics studies, where large, high-dimensional datasets, like those collected at the Large Hadron Collider, hold the key to new discoveries. Common approaches to assessing systematic uncertainties rely on simplifications, such as assuming that the impact of the various sources of uncertainty factorizes. In this paper, we provide realistic example scenarios in which this assumption fails. We introduce an algorithm that uses Gaussian process (GP) regression to estimate the impact of systematic uncertainties without assuming factorization. The GP models are enhanced with derivative information, which increases the accuracy of the regression without increasing the number of samples. We also present a novel sampling strategy based on Bayesian experimental design, which is shown to be more efficient than random and grid sampling in our example scenarios. We apply this approach to the estimation of the efficiency as a function of 2 and 4 jet energy scale parameters, demonstrating significant improvements over a more traditional approach that assumes factorization: the mean squared errors are reduced by factors of 80–120 in the 2D case, and 6–13 in the 4D case.