Bayesian rhythmic model for jointly detecting circadian biomarkers and predicting molecular circadian time in human post-mortem brain transcriptome

Transcriptomic circadian analysis of human post-mortem brain provides a unique opportunity to characterize in vivo molecular circadian rhythms across brain regions implicated in aging and psychiatric disorders. A primary goal in such analyses is the detection of circadian biomarkers. However, this task is complicated by the frequent mismatch between a subjects recorded circadian clock time and their true molecular circadian time -- arising from observational or recording errors, as well as intrinsic biological variability. Existing methods typically address either biomarker detection or circadian time prediction in isolation. Because errors in one task can degrade performance in the other, the lack of a unified approach remains a key limitation. We propose BayCT -- a Bayesian model for simultaneous circadian marker detection and molecular circadian time estimation. The model extends naturally to repeated measurements from multiple brain regions or organs. For circular data, we employ a von Mises prior distribution, with slice sampling and reversible-jump Markov chain Monte Carlo (MCMC) for Bayesian inference. Through extensive simulations and applications to transcriptomic data from three human brain regions and from 12 mouse organs, BayCT demonstrates superior performance in both biomarker detection and circadian time estimation. Furthermore, we highlight the advantages of integrating data across brain regions, achieving substantial improvements in both tasks.