  Variational Bayesian (VB) methods produce posterior inference in a time frame
considerably smaller than traditional Markov Chain Monte Carlo approaches.
Although the VB posterior is an approximation, it has been shown to produce
good parameter estimates and predicted values when a rich classes of
approximating distributions are considered. In this paper we propose Updating
VB (UVB), a recursive algorithm used to update a sequence of VB posterior
approximations in an online setting, with the computation of each posterior
update requiring only the data observed since the previous update. An extension
to the proposed algorithm, named UVB-IS, allows the user to trade accuracy for
a substantial increase in computational speed through the use of importance
sampling. The two methods and their properties are detailed in two separate
simulation studies. Two empirical illustrations of the proposed UVB methods are
provided, including one where a Dirichlet Process Mixture model with a novel
posterior dependence structure is repeatedly updated in the context of
predicting the future behaviour of vehicles on a stretch of the US Highway 101.
