Time series data appear in many areas, such as economics, audio analysis, video streaming, and biomedicine. Probabilistic models are popular tools to describe the characteristics of time series because they can capture noise effects and variations among subjects. The models based on Bayesian statistics are powerful thanks to their capabilities in performing learning, inference, and prediction. This book presents comprehensive methodologies for analyzing time series via Bayesian statistics. It is a collection of papers written by experts in the field. Readers must have a background in probability and stochastic processes to digest this book without difficulties.

Chapter 1 provides an overview of Bayesian statistics for time series analysis. The remainder of the book consists of six parts, each of which addresses a framework of time series modeling.

Part 1 (chapters 2 through 4) introduces Monte Carlo methods, which are techniques for approximate inference in probabilistic models. This part covers Markov chain Monte Carlo methods, particle filtering, and diffusion processes.

In contrast to Part 1, which focuses on probabilistic approximations, Part 2 (chapters 5 through 8) presents deterministic approximations. The authors cover variational approximations, continuous-time Markov processes, and switching linear dynamical systems.

Part 3 (chapters 9 and 10) addresses switching models. Probabilistic models are usually characterized by parameters. When the parameters change over time, we need a method to model such changes. This part presents techniques to model parameter dynamics and their applications in biomedicine.

Chapters 11 through 13 constitute Part 4, which concerns multi-object models. In many applications, the time series data comes from the aggregated movement of groups. For example, stock prices move in a group, and crowds in a video walk in a similar direction. We can utilize multi-object models to identify how groups move over time.

Part 5 (chapters 14 through 16) focuses on nonparametric models. Many applications cannot be modeled by known probabilistic processes, and nonparametric models are alternatives to describe the data. This part discusses various methods, for example, nonparametric hidden Markov models and sampling of Gaussian processes. The authors also provide examples that show how these methods can be applied to solve real problems.

The last part (chapters 17 and 18) presents agent-based models. Modern control theory recasts the control problem as an inference problem. Therefore, many machine learning techniques can be applied to solve control problems. For example, control policies can be learned and adapted in Markov decision problems.

In summary, this book is well organized. The experts in this field provide both breadth and depth. The book is suitable for statisticians, engineers, and computer scientists. Readers can definitely learn state-of-the-art techniques from it.