Automatic differentiation for error analysis

TL;DR

ADerrors.jl is a Julia software tool that uses automatic differentiation to perform precise linear error propagation in Monte Carlo data analysis, especially useful in Lattice QCD and non-linear fitting scenarios.

Contribution

The paper introduces ADerrors.jl, a novel software that enables exact linear error propagation with automatic differentiation, handling correlated data and iterative algorithms.

Findings

Exact error propagation achieved through automatic differentiation.

Software supports uncertainties in fit parameters and correlated data.

Available for download at provided URL.

Abstract

We present ADerrors.jl, a software for linear error propagation and analysis of Monte Carlo data. Although the focus is in data analysis in Lattice QCD, where estimates of the observables have to be computed from Monte Carlo samples, the software also deals with variables with uncertainties, either correlated or uncorrelated. Thanks to automatic differentiation techniques linear error propagation is performed exactly, even in iterative algorithms (i.e. errors in parameters of non-linear fits). In this contribution we present an overview of the capabilities of the software, including access to uncertainties in fit parameters and dealing with correlated data. The software, written in julia, is available for download and use in https://gitlab.ift.uam-csic.es/alberto/aderrors.jl