NoisySignalIntegration.jl: A Julia package for uncertainty evaluation of numeric integrals

Abstract

The evaluation of peak or band areas is a recurring task in scientific data evaluation. For example, in molecular spectroscopy, absorption line or band areas are often used to deter- mine substance abundance. NoisySignalIntegration.jl provides functionality to evaluate such signal areas and associated uncertainties using a Monte-Carlo approach. Uncertainties may include contributions from (potentially correlated) Gaussian noise, baseline subtraction, and uncertainty in placing integration bounds. Uncertain integration bounds can be defined in several ways to constrain the integration based on the physical system under investigation (asymmetric signals, symmetric signals, signals with identical width). The package thus offers a more objective uncertainty evaluation than a statement based on experience or laborious manual analysis (Gottschalk et al., 2018). NoisySignalIntegration.jl includes a detailed documentation that covers the typical workflow with several examples. The API uses custom datatypes and convenience functions to aid the data analysis and permits flexible customizations: Any probability distribution from Dis- tributions.jl (Besançon et al., 2021; Lin et al., 2019) is a valid input to express uncertainty in integration bounds, thus allowing to adapt the uncertainty analysis as needed to ones state of knowledge. The core integration function can be swapped if the included trapezoidal integration is deemed unsatisfactory in terms of accuracy. The package uses MonteCarloMea- surements.jl (Bagge Carlson, 2020) to express uncertain numbers which enables immediate uncertainty propagation.