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.