\begin{document}$ \beta $\end{document} decay of 205Tl at the Experimental Storage Ring (ESR) at GSI, Darmstadt, has recently been reported, with substantial impact on the use of 205Pb as an early Solar System chronometer and on the low-energy measurement of the solar neutrino spectrum via the LOREX project. Owing to the technical challenges in producing a high-purity 205Tl81+ secondary beam, a robust statistical method was developed to estimate the variation in the contaminant 205Pb81+ produced in the fragmentation reaction, which was subsequently transmitted and stored in the ESR. Here, we show that Bayesian and Monte Carlo methods produce comparable estimates for the contaminant variation, each with unique advantages and challenges given the complex statistical problems for this experiment. We recommend the adoption of such methods in future experiments that exhibit unknown statistical fluctuations."> Bayesian and Monte Carlo approaches to estimating uncertainty for the measurement of the bound-state <i>β</i><sup>-</sup> decay of <sup>205</sup>Tl<sup>81+</sup> -
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