Epidemiological contact network models have emerged as an important tool in understanding and predicting spread of infectious disease, due to their capacity to engage individual heterogeneity that may underlie essential dynamics of a particular host-pathogen system. Just as fundamental are the changes that real-world contact networks undergo over time, both independently of and in response to pathogen spreading. These dynamics play a central role in determining whether a disease will die out or become epidemic within a population, known as the epidemic threshold. In this paper, we provide an overview of methods to predict the epidemic threshold for temporal contact network models, and discuss areas that remain unexplored.

The bootstrap is a popular and powerful method for assessing precision of estimators and inferential methods. However, for massive datasets that are increasingly prevalent, the bootstrap becomes prohibitively costly in computation and its feasibility is questionable even with modern parallel computing platforms. Recently, Kleiner and co-authors proposed a method called BLB (bag of little bootstraps) for massive data, which is more computationally scalable with little sacrifice of statistical accuracy. Building on BLB and the idea of fast double bootstrap, we propose a new resampling method, the subsampled double bootstrap, for both independent data and time series data. We establish consistency of the subsampled double bootstrap under mild conditions for both independent and dependent cases. Methodologically, the subsampled double bootstrap is superior to BLB in terms of running time, more sample coverage, and automatic implementation with less tuning parameters for a given time budget. Its advantage relative to BLB and bootstrap is also demonstrated in numerical simulations and a data illustration. Supplementary materials for this article are available online.

Many real-world networks are theorized to have core-periphery structure consisting of a densely-connected core and a loosely-connected periphery. While this phenomenon has been extensively studied in a range of scientific disciplines, it has not received sufficient attention in the statistics community. In this expository article, our goal is to raise awareness about this topic and encourage statisticians to address the many open inference problems in this area. To this end, we first summarize the current research landscape by reviewing the metrics and models that have been used for quantitative studies on core-periphery structure. Next, we formulate and explore various inferential problems in this context, such as estimation, hypothesis testing, and Bayesian inference, and discuss related computational techniques. We also outline the multidisciplinary scientific impact of core-periphery structure in a number of real-world networks. Throughout the article, we provide our own interpretation of the literature from a statistical perspective, with the goal of prioritizing open problems where contribution from the statistics community will be most effective and important.