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Theoretical Aspects of Spatial-Temporal Modeling

  • Book
  • © 2015

Overview

Editors:
  1. Gareth William Peters

    1. Department of Statistical Science, University College London, London, United Kingdom

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    You can also search for this editor in PubMed   Google Scholar

  2. Tomoko Matsui

    1. The Institute of Statistical Mathematics, Tachikawa, Japan

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    You can also search for this editor in PubMed   Google Scholar

  • Covers specialized topics in spatial-temporal modeling provided by world experts for an introduction to key components
  • Discusses a rigorous probabilistic and statistical framework for a range of contemporary topics of importance to a diverse number of fields in spatial and temporal domains
  • Includes efficient computational statistical methods to perform analysis and inference in large spatial temporal application domains
  • Includes supplementary material: sn.pub/extras

Part of the book series: SpringerBriefs in Statistics (BRIEFSSTATIST)

Part of the book sub series: JSS Research Series in Statistics (JSSRES)

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Table of contents (4 chapters)

  1. Front Matter

    Pages i-xv
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  2. Particle Association Measures and Multiple Target Tracking

    • Pierre Del Moral, Jeremie Houssineau
    Pages 1-30

  3. An Overview of Recent Advances in Monte-Carlo Methods for Bayesian Filtering in High-Dimensional Spaces

    • François Septier, Gareth W. Peters
    Pages 31-61

  4. Spectral Measures of \(\alpha \)-Stable Distributions: An Overview and Natural Applications in Wireless Communications

    • Nourddine Azzaoui, Laurent Clavier, Arnaud Guillin, Gareth W. Peters
    Pages 63-94

  5. Networks, Random Graphs and Percolation

    • Philippe Deprez, Mario V. Wüthrich
    Pages 95-124
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About this book

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 geometryfeatures.

Editors and Affiliations

  • Department of Statistical Science, University College London, London, United Kingdom

    Gareth William Peters

  • The Institute of Statistical Mathematics, Tachikawa, Japan

    Tomoko Matsui

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