Preface to the Themed Issue on ‘Statistical Network Science and Its Applications’
这篇前言介绍了统计网络科学专题刊的10篇论文，涵盖网络实验设计、隐私保护、缺失数据处理、交通延迟、国际贸易、金融波动、脑网络变化点检测等应用，旨在探索不同领域网络模型与推断方法的共通性。
In recent years networks have appeared as a useful paradigm for describing processes in various domains, such as biology, sociology, epidemiology, finance and telecommunications. The data that are collected for those applications have led to the development of stochastic models for statistical network inference. These models are often specifically motivated and developed for a certain application and thus far there have been few attempts to consider the commonalities between the various network models and inference techniques. The aim of this issue, therefore, is to begin to obtain an insight into statistical methods for network-like data and processes in various applications and to explore possible bridges between the different methods that are used in the different fields. This issue contains 10 papers, which present a panorama on modern statistical network techniques. We have ordered them in a way that shows continuity of the type of questions that are considered or the types of network models and statistical methods that were employed. Just as philosophers are sometimes likened to midwives of wisdom, the job of an applied statistician starts by helping in the design of an experiment. Parker and his colleagues consider experimental design in a network context. If data are collected on a number of subjects who are connected by means of a (social) network, it might reasonably be expected that the dependences of the data follow this structure. Determining carefully how to assign treatments to individuals across a social network can improve the estimation of the treatment effects, as Parker and his colleagues explain in the opening paper of the issue. A problem of collecting data on individuals including social network information is that traditional anonymity safeguards, such as replacing identification tags, may not be sufficient any more: the network structure in combination with other covariate data may be able to trace the identity back to an individual. The competing demands for privacy and using social network information is the topic of the paper by Karwa and his colleagues, who devise a method involving exponential random-graph models that allows use of this information, while protecting the privacy of the individuals involved. An example of such a study is the National Longitudinal Study of Adolescent Health, in which a cohort of American schoolchildren in grades 7–12 were followed with the intent of determining the forces that may influence adolescent's health and risk behaviours. Gile and Handcock study these data with a specific focus on friendship determination. However, the data contain non-responding subjects, potentially resulting in an observed network that has 21% missing edges. Their paper is aimed at developing ways to deal with missing network data in the framework of an exponential random-graph model. Traffic is a typical network phenomenon: it moves across fixed, prespecified arteries and, as a consequence, it has the much dreaded potential for delays and queues. The field of delay source detection is currently part of deterministic operational research. That Manitz and co-authors introduce statistical methods to deal with this question does finally do justice to the stochastic nature of the underlying process. Trade networks have strongly impacted the modern world. Nations trade with one another to share resources and to improve the lives of their citizens. However, international trade is sometimes seen as a potential danger to the economical activity within a country, resulting in tariffs and regulation. After the Second World War, the General Agreement on Tariffs and Trade was introduced to stimulate trade. There has been significant controversy whether or not the General Agreement on Tariffs and Trade had any influence on bilateral trade. Arpino and co-authors approach this as a causal question in the context of the potential outcome or propensity score approach. Durante and his colleagues consider the economical context of consumer choice. In their paper, they develop a dedicated Bayesian model to predict monoproduct customers’ future choices in view of devising targeted advertising for cross-selling strategies. Data on both customers’ choices and co-subscription networks for a number of agencies within a company allow them to devise a clustering approach so that a small number of interpretable strategies can be extracted. Another way of looking at international trade and marketing strategies is to study the dynamic interrelatedness of individual stock prices. This is quite timely, as the period between 2000 and now has seen great volatility in the financial markets. Barigozzi and Hallin study the data between 2000 and 2013 to see whether there is any evidence for changes in the underlying structure of the markets. In their framework, the network structure is unknown and to be inferred. Using vector auto-regressive models they find that, particularly in the period immediately before the 2008 crisis, there were indeed important changes to the global financial system. The contribution by Cribben and Yu also considers multivariate time series with a similar objective of finding change points in an underlying brain network structure. This problem is extensively studied in univariate time series modelling but not in temporal network data. Cribben and Yu consider the case of interconnected brain regions measured across time through functional magnetic resonance imaging; after clustering brain regions they use a geometric approach involving principal angles to detect network change points iteratively. Network detection by using graphical models has so far been almost exclusively addressed with frequentist approaches, such as L1-regularized inference, which can scale up to networks with a large number of nodes. The drawback of such approaches is the failure to explore the possible multimodality of the likelihood. In their paper Mohammadi and co-authors develop a Bayesian transdimensional inference procedure for non-Gaussian graphical models. They achieve computational efficiency with a carefully designed birth–death Markov chain Monte Carlo algorithm. Their work is motivated by a medical application about the detection of risk factors affecting Dupuytren disease. Partial correlation coefficients play an important role in graphical models. Roverato and Castelo, in the final paper of this issue, address a fundamental question about the interpretation of these coefficients and go on to develop an alternative to partial correlation that takes into account the overall network structure. They apply this new measure in a genomic application leading to new insight about the role of individual edges in a graphical model. The field of statistical network science has three related, but distinct focuses. The papers by Karwa and his colleagues and Gile and Handcock aim to use or model the underlying random network. The use of exponential random-graph models and other random-network models is a common feature here. For Manitz and her colleagues and Arpino and his colleagues, in contrast, the network structure is given and the random process plays out on the edges of the network, such as train delays and international trade. For the experimental design paper by Parker and his colleagues the network is also fixed and given, but the stochasticity lies in the process on the vertices of the network. For the last five papers of the issue the additional complication is that the underlying network is unknown. The authors for correspondence of the 10 papers were invited to spend a week at the Isaac Newton Institute in Cambridge and to present their work during that week at a workshop as part of the ’Theoretical foundations for statistical network analysis’ programme. The event gave further opportunities for the authors and participants to discuss possible bridges between the different approaches across the different applied disciplines. To take this further, all participants as well as you, the interested reader, are encouraged to take part in a recently funded European initiative (the European Cooperation for Statistics of Network Data Science: http://www.cost.eu/COST__Actions/ca/CA15109), which, between 2016 and 2020, will provide many opportunities for training and networking for scientists working in the field of statistical network science. Preparing this issue has given us and, we hope, will give you the reader a broad perspective of statistical network science and of how statistics can contribute to this field in different applications and in different ways, from experimental design to stochastic network modelling and statistical inference. Veronica Vinciotti and Ernst Wit thank the Isaac Newton Institute for Mathematical Sciences, Cambridge, for its hospitality during the programme ‘Theoretical foundations of statistical network analysis’, which was supported by the Engineering and Physical Sciences Research Council grant EP/K032208/1.