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This paper introduces CUQIpy, a versatile open-source Python package forcomputational uncertainty quantification (UQ) in inverse problems, presented asPart I of a two-part series. CUQIpy employs a Bayesian framework, integratingprior knowledge with observed data to produce posterior probabilitydistributions that characterize the uncertainty in computed solutions toinverse problems. The package offers a high-level modeling framework withconcise syntax, allowing users to easily specify their inverse problems, priorinformation, and statistical assumptions. CUQIpy supports a range of efficientsampling strategies and is designed to handle large-scale problems. Notably,the automatic sampler selection feature analyzes the problem structure andchooses a suitable sampler without user intervention, streamlining the process.With a selection of probability distributions, test problems, computationalmethods, and visualization tools, CUQIpy serves as a powerful, flexible, andadaptable tool for UQ in a wide selection of inverse problems. Part II of theseries focuses on the use of CUQIpy for UQ in inverse problems with partialdifferential equations (PDEs).

CUQIpy -- Part I: computational uncertainty quantification for inverse problems in Python