Statistical Computations on Biological Rhythms I: Dissecting Variable Cycles and Computing Signature Phases in Activity-Event Time Series

Abstract

We propose a computational methodology to compute and extract circadian rhythmic patterns from an individual animal’s activity-event time series. This lengthy dataset, composed of a sequential event history, contains an unknown number of latent rhythmic cycles of varying duration and missing waveform information. Our computations aim at identifying the onset signature phase which individually indicates a sharp event intensity surge, where a subject-night ends and a brand new cycle’s subject-day begins, and collectively induces a linearity manifesting the individual circadian rhythmicity and information about the average period. Based on the induced linearity, the least squares criterion is employed to choose an optimal sequence of computed onset signature phases among a finite collection derived from the hierarchical factor segmentation (HFS) algorithm. The multiple levels of coding schemes in the HFS algorithm are designed to extract contrasting patterns of aggregation against sparsity of activity events along the entire temporal axis. This optimal sequence dissects the whole time series into a sequence of rhythmic cycles without model assumptions or ad hoc behavioral definitions regarding the missing waveform information. The performance of our methodology is favorably compared with two popular approaches based on the periodogram in a simulation study and in real data analyses. The computer code and data used in this article are available on the JCGS webpage.