功率谱显著性估计的贝叶斯方法及其在太阳中微子数据中的应用
A Bayesian approach to power-spectrum significance estimation, with application to solar neutrino data
摘要：
估计功率谱中峰值的显著性的通常程序是计算偶然获得该值或更大值的概率，假设时间序列仅包含噪声（例如，测量值来自高斯分布的随机采样）。然而，众所周知，人们应该谨慎对待这种P值方法。作为一种替代方案，我们在这里研究贝叶斯方法来估计功率谱中峰值的重要性。这种方法要求我们明确地考虑时间序列包含周期性信号以及噪声的假设。挑战在于确定适合该假设的功效的概率分布函数。我们提出什么似乎是合理的条件，要求这个功能，然后提出一个简单的功能，满足这些要求。我们还提出了一个一致性条件，并检查我们的函数是否满足这个条件。我们发现，贝叶斯显著性估计是相当保守的比传统的估计。我们将此程序应用于最近的三个太阳中微子数据分析：（a）双峰的GALLEX数据;（b）功率谱分析的超级神冈数据;和（c）放射化学中微子数据和辐照度数据的综合分析。
英文摘要：
The usual procedure for estimating the significance of a peak in a power spectrum is to calculate the probability of obtaining that value or a larger value by chance, on the assumption that the time series contains only noise (e.g. that the measurements were derived from random samplings of a Gaussian distribution). However, it is known that one should regard this P-Value approach with caution. As an alternative, we here examine a Bayesian approach to estimating the significance of a peak in a power spectrum. This approach requires that we consider explicitly the hypothesis that the time series contains a periodic signal as well as noise. The challenge is to identify a probability distribution function for the power that is appropriate for this hypothesis. We propose what seem to be reasonable conditions to require of this function, and then propose a simple function that meets these requirements. We also propose a consistency condition, and check to see that our function satisfies this condition. We find that the Bayesian significance estimates are considerably more conservative than the conventional estimates. We apply this procedure to three recent analyses of solar neutrino data: (a) bimodality of GALLEX data; (b) power spectrum analysis of Super-Kamiokande data; and (c) the combined analysis of radiochemical neutrino data and irradiance data.
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