The University of Southampton
Southampton Statistical Sciences Research Institute

# Professor Li-Chun Zhang has published a new book Graph Sampling with CRC Press

Published: 25 February 2022

Professor Li-Chun Zhang has published a new book Graph Sampling with CRC Press. The book establishes a sampling theory framework that unifies the key elements in the pioneering works of Birnbaum & Sirken, O. Frank and S. Thompson, and develops new strategies of probability sampling where the population units (i.e. nodes in a graph) are connected by the edges in the graph. This has applications in a wide range of areas, including social networks, internet, epidemiological and biomedical studies, graph-based machine learning, environmental and spatial statistics, etc.

Finite population sampling has found numerous applications in the past century. The validity of sampling 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). This is the key theoretical justification for its universal applicability.

A valued graph is a more powerful representation, which allows one to incorporate the connections among the population units in addition to the units on their own. The underlying structure is a graph given as a finite collection of nodes (units) and edges (connections). Attaching measures to the nodes or edges or both yields a valued graph.

Many technological, socio-economic and biological phenomena exhibit a 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 is a statistical approach to study real graphs. Just like finite population sampling, it is universally applicable based on exploring the variation over all possible subgraphs (i.e. sample graphs), which can be taken from the given population graph, according to a specified method of sampling.

Graph sampling encompasses finite population sampling as a special case. All the so-called “unconventional” finite population sampling techniques, such as indirect, network, adaptive cluster or line-intercept sampling, can be more effectively studied as special cases of graph sampling. It yields a rigorous approach to genuine graph problems, where the interest of estimation is given directly as  graph parameters, allowing one to devise and make use of various probabilistic  breadth- or depth-first non-exhaustive graph traversal algorithms.

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