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The usual procedure for estimating the significance of a peak in a powerspectrum is to calculate the probability of obtaining that value or a largervalue by chance, on the assumption that the time series contains only noise(e.g. that the measurements were derived from random samplings of a Gaussiandistribution). However, it is known that one should regard this P-Valueapproach with caution. As an alternative, we here examine a Bayesian approachto estimating the significance of a peak in a power spectrum. This approachrequires that we consider explicitly the hypothesis that the time seriescontains a periodic signal as well as noise. The challenge is to identify aprobability distribution function for the power that is appropriate for thishypothesis. We propose what seem to be reasonable conditions to require of thisfunction, and then propose a simple function that meets these requirements. Wealso propose a consistency condition, and check to see that our functionsatisfies this condition. We find that the Bayesian significance estimates areconsiderably more conservative than the conventional estimates. We apply thisprocedure to three recent analyses of solar neutrino data: (a) bimodality ofGALLEX data; (b) power spectrum analysis of Super-Kamiokande data; and (c) thecombined analysis of radiochemical neutrino data and irradiance data.

A Bayesian approach to power-spectrum significance estimation, with application to solar neutrino data