发表机构
INFN, Sezione di Padova; Luleå University of Technology（意大利国家核物理研究所帕多瓦分部; 吕勒奥理工大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究揭示了贪婪凸起偏差与别处效应源于信号模板族的局部几何，通过高斯匹配滤波模型推导了偏差分解关系，明确了局部维度等因素在偏差中的作用。
AI 中文摘要
当拟合位置或形状未知的局域信号时，通常会允许这些参数与信号振幅一同变化，并选择使似然最大的值。这种自由度会产生两个相关的统计结果：若存在真实信号，其拟合振幅会受到正偏差影响；若不存在真实信号，相同的自由度会增加发现异常类信号背景涨落的概率，从而产生别处效应。我们表明，这两种效应可被理解为信号模板族相同局部几何的结果。我们在高斯匹配滤波模型中研究这种联系，其中平滑的D维归一化模板族描述未知信号的位置或形状。在归一化匹配滤波问题中，真实信号峰的曲率和决定高背景峰曲率的涨落由同一模板度量控制，这使我们能推导出显式渐近关系。随后我们将问题从强信号和高阈值极限中分离出来：将与信号相关的最大值与最佳竞争最大值分开，可将全局偏差精确分解为局部剖析贡献和远程峰竞争贡献。在一维高斯示例中，二阶阶乘累积量占该修正的大部分，而三阶累积量使预测与模拟结果高度吻合；两点Kac-Rice计算重现了二阶累积量，并揭示了附近最大值的四次方短程抑制。所得图景在统一框架内区分了局部维度、模型相关曲率和全局极值竞争的作用。
英文摘要
When fitting a localized signal whose position or shape is not known in advance, one typically allows these parameters to vary together with the signal amplitude and chooses the values that maximize the likelihood. This freedom has two related statistical consequences. If a genuine signal is present, its fitted amplitude will be affected by a positive bias; otherwise, the same freedom increases the chance of finding an unusually signal-like background fluctuation, giving rise to the look-elsewhere effect. We show that these two effects can be understood as consequences of the same local geometry of the family of signal templates. We study this connection in a Gaussian matched-filter model, where a smooth D-dimensional family of normalized templates describes the unknown signal location or shape. In the normalized matched-filter problem, the curvature of a genuine signal peak and the fluctuations that determine the curvature of a high background peak are governed by the same template metric. This allows us to derive an explicit asymptotic relation. We then follow the problem away from the strong-signal and high-threshold limits. Separating the signal-associated maximum from the best competing maximum gives an exact decomposition of the global bias into a local profiling contribution and a contribution from remote-peak competition. In a one-dimensional Gaussian example, the second factorial cumulant accounts for most of this correction, while the third brings the prediction into close agreement with simulation. A two-point Kac--Rice calculation reproduces the second cumulant and reveals a quartic short-distance suppression of nearby maxima. The resulting picture separates the roles of local dimension, model-dependent curvature, and global extremal competition within a common framework.
Comments42 pages, 5 figures, 2 appendices
