Bayesian modeling techniques enable sensitivity analyses that incorporate detailed expectations regarding future experiments. A model-based approach also allows one to evaluate inferences and predicted outcomes, by calibrating (or measuring) the consequences incurred when certain results are reported. We present procedures for calibrating predictions of an experiment's sensitivity to both continuous and discrete parameters. Using these procedures and a new Bayesian model of the $\beta$-decay spectrum, we assess a high-precision $\beta$-decay experiment's sensitivity to the neutrino mass scale and ordering for one assumed design scenario. We find that such an experiment could measure the electron-weighted neutrino mass within $\sim 40$ meV after 1 year (90% credibility). Neutrino masses $>500$ meV could be measured within $\approx 5$ meV. Using only $\beta$ decay and external reactor neutrino data, we find that next-generation $\beta$-decay experiments could potentially constrain the mass ordering using a two-neutrino spectral model analysis. By calibrating mass ordering results, we identify reporting criteria that can be tuned to suppress false ordering claims. In some cases, a two-neutrino analysis can reveal that the mass ordering is inverted, an unobtainable result for the traditional one-neutrino analysis approach.

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未来β衰变实验对中微子质量尺度和排序敏感性的贝叶斯分析

贝叶斯建模技术支持敏感性分析，其中包含对未来实验的详细预期。基于模型的方法还允许人们通过校准（或测量）报告某些结果时产生的后果来评估推论和预测结果。我们提出了校准对连续和离散参数的实验敏感性预测的程序。使用这些程序和新的贝叶斯模型$\beta$- 衰变谱，我们评估一个高精度 $\beta$- 衰变实验对中微子质量尺度的敏感性和一种假设设计场景的排序。我们发现这样的实验可以测量内部的电子加权中微子质量$～40$ 1 年后的 meV（可信度为 90%）。中微子质量$>500$ meV 可以在 $\approx 5$ meV。仅使用$\beta$ 衰变和外部反应堆中微子数据，我们发现下一代 $\beta$- 衰变实验可能会使用双中微子光谱模型分析来限制质量排序。通过校准批量订购结果，我们确定了可以调整以抑制虚假订购声明的报告标准。在某些情况下，双中微子分析可以揭示质量排序是颠倒的，这是传统单中微子分析方法无法获得的结果。