Wavelet spectral testing: application to nonstationary circadian rhythms

TL;DR

This paper introduces wavelet spectral testing methods for analyzing nonstationary circadian rhythms, enabling more accurate detection of differences in biological signals over time.

Contribution

The authors develop novel wavelet spectral hypothesis tests for nonstationary processes, specifically tailored for circadian rhythm analysis, incorporating replicate information and evolutionary spectra estimation.

Findings

Method outperforms existing approaches in simulations.

Successfully detects spectral differences in real circadian datasets.

Facilitates broader analysis of rhythmic biological data.

Abstract

Rhythmic data are ubiquitous in the life sciences. Biologists need reliable statistical tests to identify whether a particular experimental treatment has caused a significant change in a rhythmic signal. When these signals display nonstationary behaviour, as is common in many biological systems, the established methodologies may be misleading. Therefore, there is a real need for new methodology that enables the formal comparison of nonstationary processes. As circadian behaviour is best understood in the spectral domain, here we develop novel hypothesis testing procedures in the (wavelet) spectral domain, embedding replicate information when available. The data are modelled as realisations of locally stationary wavelet processes, allowing us to define and rigorously estimate their evolutionary wavelet spectra. Motivated by three complementary applications in circadian biology, our new methodology allows the identification of three specific types of spectral difference. We demonstrate the advantages of our methodology over alternative approaches, by means of a comprehensive simulation study and real data applications, using both published and newly generated circadian datasets. In contrast to the current standard methodologies, our method successfully identifies differences within the motivating circadian datasets, and facilitates wider ranging analyses of rhythmic biological data in general.