  In this publication, we combine two Bayesian non-parametric models: the
Gaussian Process (GP) and the Dirichlet Process (DP). Our innovation in the GP
model is to introduce a variation on the GP prior which enables us to model
structured time-series data, i.e. data containing groups where we wish to model
inter- and intra-group variability. Our innovation in the DP model is an
implementation of a new fast collapsed variational inference procedure which
enables us to optimize our variationala pproximation significantly faster than
standard VB approaches. In a biological time series application we show how our
model better captures salient features of the data, leading to better
consistency with existing biological classifications, while the associated
inference algorithm provides a twofold speed-up over EM-based variational
inference.
