Graph Sampling

138 Pages·2021·3.472 MB·English

by  Li-Chun Zhang

GRAPH
SAMPLING
Taylor & Francis
Taylor & Francis Group
http://taylorandfrancis.com
GRAPH
SAMPLING
Li-Chun Zhang
First edition published 2022
by CRC Press
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© 2022 Li-Chun Zhang
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ISBN: 9781032067087 (hbk)
ISBN: 9781032067094 (pbk)
ISBN: 9781003203490 (ebk)
DOI: 10.1201/9781003203490
Publisher’s note: This book has been prepared from camera-ready copy provided by
the authors
To my parents
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Contents
Preface ix
Author Bio xi
Abbreviations xiii
Symbols xv
Chapter 1(cid:4) General introduction 1
1.1 SAMPLINGFROMFINITEPOPULATIONS 1
1.2 GRAPH,MOTIF,GRAPHPARAMETER 2
1.3 OBSERVATIONPROCEDURE 7
1.4 SAMPLE GRAPH, SAMPLING METHOD AND
SAMPLINGSTRATEGY 15
BIBLIOGRAPHICNOTES 17
Chapter 2(cid:4) Bipartite incidence graph sampling and
weighting 19
2.1 BIPARTITEINCIDENCEGRAPHSAMPLING 19
2.2 INCIDENCEWEIGHTINGESTIMATOR 21
2.3 RAO-BLACKWELLISATION 26
2.4 ILLUSTRATIONS 29
BIBLIOGRAPHICNOTES 36
vii
viii (cid:4) Contents
Chapter 3(cid:4) Strategy BIGS-IWE 39
3.1 APPLICABILITY 39
3.2 NETWORKSAMPLING 41
3.3 LINE-INTERCEPTSAMPLING 43
3.4 SAMPLINGFROMRELATIONALDATABASES 48
BIBLIOGRAPHICNOTES 51
Chapter 4(cid:4) Adaptive cluster sampling 53
4.1 SPATIALACS 53
4.2 EPIDEMICPREVALENCEESTIMATION 60
4.3 ACSDESIGNSOVERTIME 66
BIBLIOGRAPHICNOTES 72
Chapter 5(cid:4) Snowball sampling 75
5.1 T-WAVESNOWBALLSAMPLING 75
5.2 STRATEGIESFORTSBS 80
5.3 ILLUSTRATIONS 86
BIBLIOGRAPHICNOTES 91
Chapter 6(cid:4) Targeted random walk sampling 93
6.1 RANDOMWALKINGRAPHS 93
6.2 TARGETEDRANDOMWALK 97
6.3 STRATEGYFORTRWSAMPLING 101
6.4 ILLUSTRATIONS 107
BIBLIOGRAPHICNOTES 112
Bibliography 113
Index 117
Preface
Finite population sampling has found numerous social, economic,
medical,environmentalandotherscientificapplicationsinthepast
century. The validity of inference of real populations derives from
the known probability sampling design under which the sample is
selected, “irrespectively of the unknown properties of the target
population studied” (Neyman, 1934).
Representingapopulationbyagraphallowsonetoincorporate
the connections or links among the population units in addition.
The links may provide effectively access to the part of the popula-
tionthatistheprimarytarget,whichisthecaseformanyso-called
unconventional sampling methods, such as indirect, network, line-
intercept or adaptive cluster sampling. Or, one may be interested
in the structure of the connections in terms of the corresponding
graph properties or parameters, such as when various breadth- or
depth-first non-exhaustive search algorithms are applied to obtain
compressed views of large, often dynamic graphs.
Graph sampling provides a statistical approach to study real
graphs from either of these perspectives. It is based on exploring
thevariationoverallpossiblesamplegraphs(orsubgraphs),which
can be taken from the given population graph by means of the
relevant known sampling probabilities.
The book can either be read as a research monograph or used
as the basis of an advanced course for post-graduate students in
statistics, mathematics and data science. It draws heavily on the
development in the last 4-5 years, much of which was carried out
jointly with Martina Patone and Melike Oguz-Alper.
Some of the work was done during the weeks when I visited
Giovanna Ranalli at the University of Perugia, which benefitted
from their Visiting Scientist Program. Finally, I thank CRC Press
Focus, in particular Acquiring Editor, Rob Calver and Editorial
ix