Inference and Learning from Data Inference

We develop a sequential version of the importance sampling technique from Chapter 33 in order to respond to streaming data, thus leading to a sequential Monte Carlo solution. The algorithm will lead to the important class of particle filters. This chapter presents the basic data model and the main construction that enables recursive inference. Many of the inference and learning methods in subsequent chapters will possess a recursive structure, which is a fundamental property to enable them to continually learn in response to the arrival of sequential data measurements. Particle filters are particularly well suited for scenarios involving nonlinear models and non-Gaussian signals, and they have found applications in a wide range of areas where these two features (nonlinearity and non-Gaussianity) are prevalent, including in guidance and control, robot localization, visual tracking of objects, and finance.