Abstract
Variational Bayesian (VB) methods usually 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 pre-dicted values when a rich class of approximating distributions are considered. In this paper wepropose Updating VB (UVB), a recursive algorithm used to update a sequence of VB posteriorapproximations in an online setting, with the computation of each posterior update requiringonly 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 computationalspeed through the use of importance sampling. The two methods and their properties are de-tailed in two separate simulation studies. Two empirical illustrations of the proposed UVBmethods are provided, including one where a Dirichlet Process Mixture model is repeatedlyupdated in the context of predicting the future behaviour of vehicles on a stretch of the USHighway 101.