AI 中文总结
该研究针对稀有事件搜寻中因模型误设导致的静默覆盖失效，提出泊松-费舍尔简并指数预测失效，通过建模变形恢复覆盖但损失灵敏度。
AI 中文摘要
低本底实验中对新物理的搜寻从少量事例中推断非负信号强度，且常报告上限。标称频率论覆盖要求区间构造有效且数据模型恰当。我们在精确泊松计数实验、暗物质反冲谱及无中微子双β衰变峰搜寻中，研究受控模型偏离对六种区间方法的下端点与上端点覆盖的影响。我们提出泊松-费舍尔简并指数 $\mathcal I_{\mathrm{PF}}(\delta\nu;\vartheta_0)=(\beta,\gamma)$，该指数在投影到完整拟合切空间后，将指定的预期计数变形映射为：$\beta$ 是轮廓标准误单位下拟合信号的带符号偏移，$\gamma$ 是未吸收残差的泊松-费舍尔范数。局部上，$\beta$ 的符号标识受威胁的端点；较大的 $\gamma$ 意味着在固定5%一类错误率下，所用的饱和泊松拟合优度检验的可检测性更高。在所研究的变形中，类信号的正偏差会降低发现侧覆盖，同时使上限偏保守；信号效率高估导致的负信号偏差可能使上端点覆盖不足。标称模拟器下的校准无法保护该模拟器相对于数据生成过程的误设。因此，具有大 $|\beta|$ 和小 $\gamma$ 的合理变形可能逃避诊断，应通过辅助信息约束的冗余参数表示，或纳入合理的包络中。在完全共线的约束冗余参数基准中，对变形建模可在评估网格点处恢复覆盖，但会以区间灵敏度的可量化损失为代价。
英文摘要
Searches for new physics in low-background experiments infer a non-negative signal strength from few events and often report an upper limit. Nominal frequentist coverage requires both a valid interval construction and an adequate data model. We study how controlled model departures affect lower- and upper-endpoint coverage for six interval procedures in an exact Poisson counting experiment, dark-matter recoil spectra, and a neutrinoless-double-beta-decay peak search. We introduce the Poisson--Fisher degeneracy index $\mathcal I_{\mathrm{PF}}(δν;\vartheta_0)=(β,γ)$, which maps a specified expected-count deformation, after projection onto the complete fitted tangent space, to $β$, the signed fitted signal shift in profiled standard-error units, and $γ$, the Poisson--Fisher norm of the unabsorbed residual. Locally, the sign of $β$ identifies the threatened endpoint, while larger $γ$ implies greater detectability by the saturated-Poisson goodness-of-fit test used here at a fixed $5\%$ type-I error rate. Across the studied deformations, positive signal-like bias degrades discovery-side coverage while making upper limits conservative; negative signal bias from overestimated signal efficiency can make the upper endpoint undercover. Calibration under the nominal simulator does not protect against misspecification of that simulator relative to the data-generating process. A plausible deformation with large $|β|$ and small $γ$ may therefore evade diagnosis and should be represented by a nuisance constrained with auxiliary information or included in a defensible envelope. In the exactly collinear constrained-nuisance benchmark, modelling the deformation restores coverage at the evaluated grid points, at a quantifiable cost in interval sensitivity.
