We present the Vida family of abstractions of anonymous communication systems, model them probabilistically and apply Bayesian inference to extract patterns of communications and user profiles. The first is a very generic Vida Black-box model that can be used to analyse information about all users in a system simultaneously, while the second is a simpler Vida Red-Blue model, that is very efficient when used to gain information about particular target senders and receivers. We evaluate the Red-Blue model to find that it is competitive with other established long-term traffic analysis attacks, while additionally providing reliable error estimates, and being more flexible and expressive.