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A powerful study design in the fields of genomics and metabolomics is the'replicated time course experiment' where individual time series are observedfor a sample of biological units, such as human patients, termed replicates.Standard practice for analysing these data sets is to fit each variable (e.g.gene transcript) independently with a functional mixed-effects model to accountfor between-replicate variance. However, such an independence assumption isbiologically implausible given that the variables are known to be highlycorrelated.  In this article we present a skew-t-normal multi-level reduced-rankfunctional principal components analysis (FPCA) model for simultaneouslymodelling the between-variable and between-replicate variance. The reduced-rankFPCA model is computationally efficient and, analogously with a standard PCAfor vectorial data, provides a low dimensional representation that can be usedto identify the major patterns of temporal variation. Using an example casestudy exploring the genetic response to BCG infection we demonstrate that theselow dimensional representations are eminently biologically interpretable. Wealso show using a simulation study that modelling all variables simultaneouslygreatly reduces the estimation error compared to the independence assumption.

A Skew-t-Normal Multi-Level Reduced-Rank Functional PCA Model with Applications to Replicated `Omics Time Series Data Sets