This book presents recent advances of Bayesian inference in structured tensor decompositions. It explains how Bayesian modeling and inference lead to tuning-free tensor decomposition algorithms, which achieve state-of-the-art performances in many applications, includingblind source separation;social network mining;image and video processing;array signal processing; and,wireless communications.The book begins with an introduction to the general topics of tensors and Bayesian theories. It then discusses probabilistic models of various structured tensor decompositions and their inference...