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This book provides a modern introductory tutorial on specialized theoretical aspects of spatial and temporal modeling. The areas covered involve a range of topics which reflect the diversity of this domain of research across a number of quantitative disciplines. For instance, the first chapter provides up-to-date coverage of particle association measures that underpin the theoretical properties of recently developed random set methods in space and time otherwise known as the class of probability hypothesis density framework (PHD filters). The second chapter gives an overview of recent advances in Monte Carlo methods for Bayesian filtering in high-dimensional spaces. In particular, the chapter explains how one may extend classical sequential Monte Carlo methods for filtering and static inference problems to high dimensions and big-data applications. The third chapter presents an overview of generalized families of processes that extend the class of Gaussian process models to heavy-tailed families known as alpha-stable processes. In particular, it covers aspects of characterization via the spectral measure of heavy-tailed distributions and then provides an overview of their applications in wireless communications channel modeling. The final chapter concludes with an overview of analysis for probabilistic spatial percolation methods that are relevant in the modeling of graphical networks and connectivity applications in sensor networks, which also incorporate stochastic geometry features.
