Wavelet spectral testing: application to nonstationary circadian rhythms

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JournalAnnals of Applied Statistics
DateAccepted/In press - 19 Feb 2019
DatePublished (current) - 17 Oct 2019
Issue number3
Number of pages30
Pages (from-to)1817-1846
Original languageEnglish


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.

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