equation pTS MMM eg Og prop
equation(2)pPooled-MMM(eg,Og)∝∑cgP(cg)(∏sp(esg cg))(∏o∈Og(P(o cg))1 Og ),where s corresponds to a stage and esg is the gene KU-57788 (sub) vector, i.e. a pool of samples encompassing time points t ∈ s . The form of p(esg cg) is a multivariate Gaussian with a diagonal covariance matrix with shared parameters, i.e. the means and variances are constrained to be the same value across all the time points of a stage. Note that similar to the MMM model, the GO tags are generated at the entire time-course level. The graphical model for the Pooled-MMM is the same as that of MMM except that the parameters across the pooled time points of a stage are shared as shown in Fig. 1.
2.4. Stage-specific multimodal mixture model (SS-MMM)
The stage-specific multimodal mixture model assumes that genes cluster independently at different biological stages, a gene’s expression values at time points within a stage being noisy versions of the same latent value. Thus we pool the samples for each stage, and assume that the observations are conditionally independent, given the stage. The joint distribution p(eg,Og)p(eg,Og) is modeled as