Bayesian inference as iterated random functions with applications to sequential inference in graphical models

The sequential posterior updates play a central role in many Bayesian inference procedures. As an example, in Bayesian inference one is interested in the posterior probability of variables of interest given the data observed sequentially up to a given time point. As a more specific example which provides the motivation for this work, in a sequential change point detection problem [1], the key quantity is the posterior probability that a change has occurred given the data observed up to present time. When the underlying probability model is complex, e.g., a large-scale graphical model, the calculation of such quantities in a fast and online manner is a formidable challenge. In such situations approximate inference methods are required - for graphical models, message-passing variational inference algorithms present a viable option [2, 3].