Gaussian process regression (GPR) has been extensively used for modelling and differential testing of biological time-series measurements due to its robustness and interpretability (Aijo and Lahdesmaki, 2009; Cooke et al., 2011). However, the standard gaussian process (Rasmussen and Williams, 2006) assumes stationary model dynamics and is a poor fit for common perturbation experiments, where we expect to see rapid changes after the perturbation and diminishing rate of state change as the cell returns back to a stable state.
A common application of time-series measurements is the testing of significant difference between two time-serie pro les (Dudoit et al., 2002). The currently used two-sample differential tests, based on gaussian processes, focus on comparing model likelihoods over a subset of measured time-points (Stegle et al., 2010; Storey et al., 2005), and hence necessitate dense measurements to cover the time axis.
We address these problems by proposing timedependent extensions to both gaussian process regression and significance analysis between time-series. We propose a time-dépendent noise model and time-dependent covariance priors (Gibbs, 1997; Pacriorek and Schervish, 2004), suitable for perturbation experiments. We utilise a novel model inference criteria for sparse measurements, which results in more informative models along time. We propose two novel differential tests for time-series, that both allow significance testing at non-observed time-points. We apply the extended GPR model for analysis of differential expression of irradiated human umbilical vein endothelial cell (HUVEC) transcriptomics dataset.