Cinderella - Comparison of INDEpendent RELative Least-squares Amplitudes

TL;DR

This paper introduces Cinderella, a statistical method for comparing frequency signals across multiple noisy data sets to determine if they originate from the same source or are due to noise, applicable in various observational contexts.

Contribution

Cinderella provides a novel statistical estimator for assessing the reality of signals across different observations, improving the reliability of frequency analysis in noisy environments.

Findings

Cinderella effectively distinguishes intrinsic signals from instrumental noise.

The method computes joint and conditional probabilities for frequency peaks across data sets.

Applications demonstrate its utility in multi-filter and multi-epoch observations.

Abstract

The identification of increasingly smaller signal from objects observed with a non-perfect instrument in a noisy environment poses a challenge for a statistically clean data analysis. We want to compute the probability of frequencies determined in various data sets to be related or not, which cannot be answered with a simple comparison of amplitudes. Our method provides a statistical estimator for a given signal with different strengths in a set of observations to be of instrumental origin or to be intrinsic. Based on the spectral significance as an unbiased statistical quantity in frequency analysis, Discrete Fourier Transforms (DFTs) of target and background light curves are comparatively examined. The individual False-Alarm Probabilities are used to deduce conditional probabilities for a peak in a target spectrum to be real in spite of a corresponding peak in the spectrum of a background or of comparison stars. Alternatively, we can compute joint probabilities of frequencies to occur in the DFT spectra of several data sets simultaneously but with different amplitude, which leads to composed spectral significances. These are useful to investigate a star observed in different filters or during several observing runs. The composed spectral significance is a measure for the probability that none of coinciding peaks in the DFT spectra under consideration are due to noise. Cinderella is a mathematical approach to a general statistical problem. Its potential reaches beyond photometry from ground or space: to all cases where a quantitative statistical comparison of periodicities in different data sets is desired. Examples for the composed and the conditional Cinderella mode for different observation setups are presented.