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

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.