Bayesian Covariate-Dependent Circadian Modeling of Rest-Activity Rhythms

Figures

• 

  Figure 1.. Simulated realizations (dots) and true generating signal (red line) for four different combinations of the modeling parameters: (a) mi=1,a(⋅)=4,αi=0,βi=10, and ϕ(⋅)=12; (b) mi=0,a(⋅)=4,αi=−0.99,βi=10, and ϕ(⋅)=4; (c) mi=1,a(⋅)=3,αi=0.99,βi=3, and ϕ(⋅)=8; (d) mi=1,a(⋅)=3,αi=0,βi=3, and ϕ(⋅)=8; for all scenarios σi2=1.

• 

  Figure 2.. Simulation study. Simulated time series data for four subjects.

• 

  Figure 3.. Simulation study. Histograms depicting subject-specific parameters mi, αi, βi, and σi, derived from posterior samples across all subjects. Vertical dotted lines denote the true parameter values.

• 

  Figure 4.. Simulation study. Scatterplots showcasing estimated values of amplitudes axi,ηa and phases ϕxi,ηϕ for i=1,…,N, alongside their corresponding true values.

• 

  Figure 5.. Simulation study. (left) Posterior probability of inclusion (PPI) for linear coefficients ηa and ηϕ; (right) Boxplots depicting the posterior distribution of effects for amplitude and phase. Horizontal blue lines represent true generating effects for non-zero coefficients.

• 

  Figure 6.. Simulation study. Marginal likelihood across 20 replicated datasets for Ti={500,1000} and σ={0.5,1,1.5,2.0}; results are displayed for CALC l1, CALC Blasso, standard cosinor, and extended cosinor (RAR).

• 

  Figure 7.. Actigraphy data. Log activity time series for four representative subjects, illustrated by dots. Shaded gray lines depict 100 draws from the posterior predictive distribution. Rectangles along the time axis indicate periods from 8pm to 8am.

• 

  Figure 8.. Actigraphy data. Scatterplots showing the relationships between each combination of parameters aX,ηa,ϕX,ηϕ,β,α,m, and σ. Histograms of the posterior samples are reported in the plots on the diagonal. Pairwise Pearson correlation coefficients are also reported.

• 

  Figure 9.. Actigraphy data. (left) Posterior probabilities of inclusion (PPIs) of the regression coefficients for amplitude, ηa, and phase, ηφ, with significant covariates highlighted in red for amplitude and blue for phase; (right) Boxplots of the posterior samples of the corresponding selected coefficients (excluding the intercepts).

• 

  Figure 10.. Actigraphy data. Scatterplots of subject-specific estimated effects on amplitudes, by significant covariates.

• 

  Figure 11.. Actigraphy data. Scatterplots of subject-specific estimated effects on phases, by significant covariates.