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Astroparticle experiments such as IceCube or MAGIC require a deconvolution oftheir measured data with respect to the response function of the detector toprovide the distributions of interest, e.g. energy spectra. In this paper,appropriate uncertainty limits that also allow to draw conclusions on thegeometric shape of the underlying distribution are determined using bootstrapmethods, which are frequently applied in statistical applications. Bootstrap isa collective term for resampling methods that can be employed to approximateunknown probability distributions or features thereof. A clear advantage ofbootstrap methods is their wide range of applicability. For instance, theyyield reliable results, even if the usual normality assumption is violated.  The use, meaning and construction of uncertainty limits to any user-specificconfidence level in the form of confidence intervals and levels are discussed.The precise algorithms for the implementation of these methods, applicable forany deconvolution algorithm, are given. The proposed methods are applied toMonte Carlo simulations to show their feasibility and their precision incomparison to the statistical uncertainties calculated with the deconvolutionsoftware TRUEE.

Uncertainty Limits on Solutions of Inverse Problems over Multiple Orders of Magnitude using Bootstrap Methods: An Astroparticle Physics Example