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

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.

💡 Research Summary

This paper delves into the analysis of peak detection in over-sampled power spectra, focusing on the concept of false-alarm probability. False-alarm probability refers to the likelihood that at least one out of M independent power values within a specified search band of a power spectrum derived from white-noise time series exceeds or equals a given value. Traditionally, this is calculated under the assumption that powers are exponentially distributed as expected for normally distributed random noise measurements.

However, in practical applications, peaks are typically examined in over-sampled power spectra. Therefore, it’s more appropriate to compare the strength of specific peaks with the distribution of peaks derived from normally distributed random noise in an over-sampled context. The paper demonstrates that this approach leads to a more conservative formula for calculating false-alarm probability.

Additionally, the paper discusses how Bayesian methods can be used to estimate the probability of the null hypothesis – that there is no oscillation within the time series. This method plays a crucial role in data analysis, especially in high-energy physics research such as with Super-Kamiokande solar neutrino data. The authors provide an example illustrating how these procedures are applied to real-world data.

The paper’s findings highlight that peak analysis methods for over-sampled power spectra offer more accurate and conservative results when calculating false-alarm probability compared to traditional formulas. This insight is particularly valuable in enhancing the understanding of critical data analysis processes in high-energy physics research.