EAN: 9784431553359

SPRINGERBRIEFS IN STATISTICS THEORETICAL ASPE...

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.

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