标题： 与过采样功率谱相关的虚警概率，应用于超级神冈探测器的太阳中微子数据 显示英文标题

标题： False-alarm probability in relation to over-sampled power spectra, with application to Super-Kamiokande solar neutrino data

摘要： “虚警概率”这一术语表示预期在由白噪声时间序列计算出的功率谱的指定搜索带内，M个独立功率值中至少有一个大于或等于某个给定值的概率。 通常使用的公式基于这样的假设：功率呈指数分布，这是对正态分布随机噪声进行功率测量时所期望的。 然而，在实际操作中，人们通常会检查过采样的功率谱中的峰值。 因此，更合适的做法是比较特定峰值的强度与从正态分布随机噪声得出的过采样功率谱中峰值的分布。 我们表明，这导致了一个比熟悉公式更为保守的虚警概率公式。 我们还展示了如何将这些结果与贝叶斯方法结合，用于估计零假设（即时间序列中没有振荡）的概率，并以超级神冈探测器太阳中微子数据为例讨论了这些程序的应用。 显示英文摘要

摘要： The term "false-alarm probability" denotes the probability that at least one out of M independent power values in a prescribed search band of a power spectrum computed from a white-noise time series is expected to be as large as or larger than a given value. The usual formula is based on the assumption that powers are distributed exponentially, as one expects for power measurements of normally distributed random noise. However, in practice one typically examines peaks in an over-sampled power spectrum. It is therefore more appropriate to compare the strength of a particular peak with the distribution of peaks in over-sampled power spectra derived from normally distributed random noise. We show that this leads to a formula for the false-alarm probability that is more conservative than the familiar formula. We also show how to combine these results with a Bayesian method for estimating the probability of the null hypothesis (that there is no oscillation in the time series), and we discuss as an example the application of these procedures to Super-Kamiokande solar neutrino data.