Handbook of Multiple Comparisons

Finite population sampling has found numerous applications in the past century. Validity inference of real populations is possible based on known sampling probabilities, “irrespectively of the unknown properties of the target population studied” (Neyman, 1934). Graphs allow one to incorporate the connections among the population units in addition. Many socio-economic, biological, spatial, or technological phenomena exhibit an underlying graph structure that may be the central interest of study, or the edges may effectively provide access to those nodes that are the primary targets. Either way, graph sampling provides a universally valid approach to studying realvalued graphs. This book establishes a rigorous conceptual framework for graph sampling and gives a unified presentation of much of the existing theory and methods, including several of the most recent developments. The most central concepts are introduced in Chapter 1, such as graph totals and parameters as targets of estimation, observation procedures following an initial sample of nodes that drive graph sampling, sample graph in which different kinds of induced subgraphs (such as edge, triangle, 4circle, K-star) can be observed, and graph sampling strategy consisting of a sampling method and an associated estimator. Chapters 2–4 introduce strategies based on bipartite graph sampling and incidence weighting estimator, which encompass all the existing unconventional finite population sampling methods, including indirect, network, adaptive cluster, or line intercept sampling. This can help to raise awareness of these methods, allowing them to be more effectively studied and applied as cases of graph sampling. For instance, Chapter 4 considers how to apply adaptive network sampling in a situation like the covid outbreak, which allows one to combat the virus spread by testtrace and to estimate the prevalence at the same time, provided the necessary elements of probability design and observation procedure are implemented. Chapters 5 and 6 deal with snowball sampling and targeted random walk sampling, respectively, which can be regarded as probabilistic breath-first or depth-first non-exhaustive search methods in graphs. Novel approaches to sampling strategies are developed and illustrated, such as how to account for the fact that an observed triangle could have been observed in many other ways that remain hidden from the realized sample graph, or how to estimate a parameter related to certain finiteorder subgraphs (such as a triangle) based on a random walk in the graph. The Bibliographic Notes at the end of each chapter contain some reflections on sources of inspiration, motivations for chosen approaches, and topics for future development. I found that the contents of the book are highly innovative and useful. The indirect sampling of Lavillee (2007) can be viewed as a special case of graph sampling. The materials in adaptive cluster sampling should be very useful in many real-world sampling problems. Some materials are not yet published elsewhere. Modern sampling research topics such as respondent-driven sampling or reinforcement learning can be viewed as a graph sampling problem. In this sense, graph sampling can be the future of sampling. However, the explanations in the book are somewhat concise. More examples and contexts will help us understand the concepts. Also, the design-based framework assumes that the conditional inclusion probabilities are known in advance. It would be great if the author could cover the situations where these inclusion probabilities are estimated rather than known. Also, a chapter on real applications would help the readers understand the materials better. I hope these contents are covered in the second edition of the book. Anyway, there is a lot to explore in this area, and the book can be a good guide for the tour of graph sampling. I plan to use the book as a reference in my course on advanced survey sampling at Iowa State University.