Theoretical Aspects of Spatial-Temporal Modeling Springerbriefs in Statistics

SPRINGER BRIEFS IN STATISTICS JSS RESEARCH SERIES IN STATISTICS Gareth William Peters Tomoko Matsui Editors Theoretical Aspects of Spatial-Temporal Modeling SpringerBriefs in Statistics JSS Research Series in Statistics Editors-in-Chief Naoto Kunitomo Akimichi Takemura Series editors Genshiro Kitagawa Tomoyuki Higuchi Nakahiro Yoshida Yutaka Kano Toshimitsu Hamasaki Shigeyuki Matsui Manabu Iwasaki The current research of statistics in Japan has expanded in several directions in line with recent trends in academic activities in the area of statistics and statistical sciences over the globe. The core of these research activities in statistics in Japan has been the Japan Statistical Society (JSS). This society, the oldest and largest academic organization for statistics in Japan, was founded in 1931 by a handful of pioneer statisticians and economists and now has a history of about 80 years. Many distinguished scholars have been members, including the influential statistician Hirotugu Akaike, who was a past president of JSS, and the notable mathematician Kiyosi Itô, who was an earlier member of the Institute of Statistical Mathematics (ISM), which has been a closely related organization since the establishment of ISM. The society has two academic journals: the Journal of the Japan Statistical Society (English Series) and the Journal of the Japan Statistical Society (Japanese Series). The membership of JSS consists of researchers, teachers, and professional statisticians in many different fields including mathematics, statistics, engineering, medical sciences, government statistics, economics, business, psychology, educa- tion, and many other natural, biological, and social sciences. The JSS Series of Statistics aims to publish recent results of current research activities in the areas of statistics and statistical sciences in Japan that otherwise would not be available in English; they are complementary to the two JSS academic journals, both English and Japanese. Because the scope of a research paper in academic journals inevitably has become narrowly focused and condensed in recent years, this series is intended to fill the gap between academic research activities and the form of a single academic paper. The series will be of great interest to a wide audience of researchers, teachers, professional statisticians, and graduate students in many countries who are interested in statistics and statistical sciences, in statistical theory, and in various areas of statistical applications. More information about this series at http://www.springer.com/series/13497 Gareth William Peters • Tomoko Matsui Editors Theoretical Aspects of Spatial-Temporal Modeling 123 Editors Gareth William Peters Tomoko Matsui Department of Statistical Science The Institute of Statistical Mathematics University College London Tachikawa, Tokyo London Japan UK ISSN 2191-544X ISSN 2191-5458 (electronic) SpringerBriefs in Statistics ISSN 2364-0057 ISSN 2364-0065 (electronic) JSS Research Series in Statistics ISBN 978-4-431-55335-9 ISBN 978-4-431-55336-6 (eBook) DOI 10.1007/978-4-431-55336-6 Library of Congress Control Number: 2015954809 Springer Tokyo Heidelberg New York Dordrecht London © The Author(s) 2015 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Printed on acid-free paper Springer Japan KK is part of Springer Science+Business Media (www.springer.com) Preface The idea to create this book arose as a response to the discussions and presentations that took place in the first and second annual international workshops on spatial and temporal modeling (STM2013 and STM2014), both of which were held in the Institute of Statistical Mathematics (ISM), Tokyo, Japan. These workshops were cohosted by Prof. Tomoko Matsui (ISM) and Dr. Gareth W. Peters (UCL). It was apparent after these workshops were completed that the wide range of participants from various backgrounds including probability, statistics, applied mathematics, physics, engineering, and signal processing as well as speech and audio processing had been recently developing a range of new theory, models, and methods for dealing with spatial and temporal problems that would be beneficial to document for a wider scientific audience. Therefore, this book is intended to bring together a range of new innovations in the area of spatial and temporal modeling in the form of self-contained tutorial chapters on recent areas of research innovations. Since it is based on contributions from a range of world experts in spatial and temporal modeling who participated in the workshop, it reflects a cross section of specialist information on a range of important related topics. It is the aim of such a text to provide a means to motivate further research, discussion, and cross-fertilization of research ideas and directions among the different research fields representative of the authors who contributed. While this book covers more of the theoretical aspects of spatial–temporal modeling, its companion book, also in the Springer Briefs series, titled Modern Methodology and Applications in Spatial-Temporal Modeling, complements this book for practitioners as it covers a range of new innovations in methodology for modeling and applications. This book aims to provide 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, Chap. 1 provides modern 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 (Ph.D. filters). v vi Preface Chapter 2 deals with an overview of recent advances in Monte Carlo methods for Bayesian filtering in high-dimensional spaces. In particular it explains how one may extend classical sequential Monte Carlo methods for filtering and static inference problems to high dimensions and big-data applications. Chapter 3 deals with 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 it then provides an overview of their applications in wireless communications channel modeling. Chapter 4 concludes with an overview of analysis for probabilistic spatial percolation methods as would be relevant in the modeling of graphical networks and connectivity applications in sensor networks which also incorporate stochastic geometry features. We first note that each chapter of this book is intended to be a self-contained research-level tutorial on modern approaches to the theoretical study of some aspect of spatial and temporal statistical modeling. However, to guide the reader in con- sidering the sections of this book we note the following relationships between chapters. Chapters 1 and 2 cover recent advances in spatial tracking and state space modeling settings in high-dimensional contexts. The first arises in multiple target tracking settings and is based on extensions of sequential Monte Carlo methods for such contexts which have become known as probability hypothesis density filters. Chapter 2 deals with the class of high-dimensional state space models and introduces different approaches one can adopt to tackle the curse of dimensionality that the standard SMC method suffers from when the state space is high dimensional. In particular it introduces ideas of blocked particle filters, discusses recent space–time particle filters and studies, and compares these to the recently developed class of methods known as sequential Markov chain Monte Carlo (SMCMC) methods. Chapters 3 and 4 are not so much focused on the estimation of latent process models in spatial–temporal settings, but instead focus on the study of phenomena that have been developed recently to characterize extremes in spatial–temporal settings. In this regard the fourth chapter discusses new approaches to the characterization of heavy-tailed stochastic processes, focusing specifically on the Preface vii α-stable family. The final chapter constructs characterizations of spatial processes from a geometrical perspective, focusing on spatial network structures, random graphs and the study of certain connectivity phenomena for such graphical structures. The chapter introduces

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