Theoretical Aspects of Spatial-Temporal Modeling

136 Pages·2015·2.822 MB·English

by  Gareth William Peters, Tomoko Matsui (eds.)

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
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Naoto Kunitomo
Akimichi Takemura
Series editors
Genshiro Kitagawa
Tomoyuki Higuchi
Nakahiro Yoshida
Yutaka Kano
Toshimitsu Hamasaki
Shigeyuki Matsui
Manabu Iwasaki
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Gareth William Peters Tomoko Matsui
(cid:129)
Editors
Theoretical Aspects
of Spatial-Temporal
Modeling
123
Editors
Gareth William Peters TomokoMatsui
Department ofStatistical Science TheInstitute of Statistical Mathematics
University CollegeLondon Tachikawa, Tokyo
London Japan
UK
ISSN 2191-544X ISSN 2191-5458 (electronic)
SpringerBriefs inStatistics
ISSN 2364-0057 ISSN 2364-0065 (electronic)
JSSResearch Series in Statistics
ISBN978-4-431-55335-9 ISBN978-4-431-55336-6 (eBook)
DOI 10.1007/978-4-431-55336-6
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Preface
Theideatocreatethisbookaroseasaresponsetothediscussionsandpresentations
thattookplaceinthefirstandsecondannualinternationalworkshopsonspatialand
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,andsignalprocessingaswellasspeechandaudioprocessing
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,thisbookisintendedtobringtogetherarangeofnewinnovationsin
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
fromarangeofworldexpertsinspatialandtemporalmodelingwhoparticipatedin
the workshop, it reflects a cross section of specialist information on a range of
importantrelatedtopics.Itistheaimofsuchatexttoprovideameanstomotivate
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
areascoveredinvolvearangeoftopicswhichreflectthediversityofthisdomainof
researchacrossanumberofquantitativedisciplines.Forinstance,Chap.1provides
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
Bayesianfilteringinhigh-dimensionalspaces.Inparticularitexplainshowonemay
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 par-
ticularitcoversaspectsofcharacterizationviathespectralmeasureofheavy-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-leveltutorialonmodernapproachestothetheoreticalstudyofsomeaspect
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.Chapters1and2coverrecentadvancesinspatialtrackingandstatespace
modeling settings in high-dimensional contexts. The first arises in multiple target
trackingsettingsandisbasedonextensionsofsequentialMonteCarlomethodsfor
such contexts which have become known as probability hypothesis density filters.
Chapter 2 deals with the class of high-dimensional state space models and intro-
duces different approachesonecanadopt totacklethecurse ofdimensionalitythat
thestandardSMCmethodsuffersfromwhenthestatespaceishighdimensional.In
particularitintroducesideasofblockedparticlefilters,discussesrecentspace–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 char-
acterization 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 struc-
tures.Thechapterintroduces ideasthat canbeusedtocharacterize andunderstand
randomgraphicalmodelsthataregrowinginpopularityintrackingmultipleobjects
and populations, finance, ecology, and social network analysis.
Tokyo, Japan Gareth William Peters
August 2015 Tomoko Matsui
Acknowledgments
WeareverygratefultoResearchOrganizationofInformationandSystems(ROIS),
The Institute of Statistical Mathematics (ISM), UK Royal Society International
Exchange Grant, and Ministry of Education, Culture, Sports, Science and
Technology (MEXT) undertake project “Cooperation with Math Program” to
supportthefirstandsecondannualinternationalworkshopsonspatialandtemporal
modeling (STM2013 and STM2014) and the first workshop on complex systems
modelingandestimationchallengesinbigdata(CSM2014).Theideatocreatethis
bookaroseasaresponsetothediscussionsandpresentationsthattookplaceinthe
workshops.
Wewouldliketoexpressoursincerethankstoallthefollowingpresentersinthe
workshops.
(cid:129) Prof. Nourddine Azzaoui, Université Blaise Pascal
(cid:129) Prof. Jen-Tzung Chien, National Chiao Tung University
(cid:129) Prof. Arnaud Doucet, Oxford University
(cid:129) Prof. Norikazu Ikoma, KIT
(cid:129) Prof. Kenji Fukumizu, ISM
(cid:129) Prof. Konstatin Markov, Aizu University
(cid:129) Prof. Daichi Mochihashi, ISM
(cid:129) Prof. Pierre Del Moral, UNSW
(cid:129) Prof. Tor Andre Myrvoll, SINTEF
(cid:129) Dr. Ido Nevat, Institute for Infocomm Research, A-Star
(cid:129) Prof. Yosihiko Ogata, ERI, University of Tokyo and ISM, ROIS
(cid:129) Dr. Takashi Owada, Technion
(cid:129) Prof. Daniel P. Palomar, HKUST
(cid:129) Prof. François Septier, Telecom lille 1
(cid:129) Prof. Taiji Suzuki, Tokyo Institute of Technology
(cid:129) Prof. Kazuya Takeda, Nagoya University
(cid:129) Prof. Mario Wüthrich, ETH Zurich
ix
Contents
1 Particle Association Measures and Multiple Target Tracking. . . . . . 1
Pierre Del Moral and Jeremie Houssineau
2 An Overview of Recent Advances in Monte-Carlo Methods for
Bayesian Filtering in High-Dimensional Spaces. . . . . . . . . . . . . . . . 31
François Septier and Gareth W. Peters
3 Spectral Measures of α-stable Distributions: An Overview and
Natural Applications in Wireless Communications. . . . . . . . . . . . . . 63
Nourddine Azzaoui, Laurent Clavier, Arnaud Guillin
and Gareth W. Peters
4 Networks, Random Graphs and Percolation . . . . . . . . . . . . . . . . . . 95
Philippe Deprez and Mario V. Wüthrich
xi