'What's going to happen next?' Time series data hold the answers, and Bayesian methods represent the cutting edge in learning what they have to say. This ambitious book is the first unified treatment of the emerging knowledge-base in Bayesian time series techniques. Exploiting the unifying framework of probabilistic graphical models, the book covers approximation schemes, both Monte Carlo and deterministic, and introduces switching, multi-object, non-parametric and agent-based models in a variety of application environments. It demonstrates that the basic framework supports the rapid creation of models tailored to specific applications and gives insight into the computational complexity of their implementation. The authors span traditional disciplines such as statistics and engineering and the more recently established areas of machine learning and pattern recognition. Readers with a basic understanding of applied probability, but no experience with time series analysis, are guided from fundamental concepts to the state-of-the-art in research and practice.