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A closed-form solution for zero-coupon bonds is obtained for a version of the discrete-time arbitrage-free Nelson-Siegel model. An estimation procedure relying on a Kalman filter is provided. The model is shown to produce adequate fit when applied to historical Canadian spot rate data and to improve distributional predictive performance over benchmarks. An adaptation of the mixed fund return model from Augustyniak et al. ((2021). ASTIN Bulletin: The Journal of the IAA, 51(1), 131–159.) is also provided to include the discrete-time arbitrage-free Nelson-Siegel model as one of its building blocks.
Complex networks are key to describing the connected nature of the society that we live in. This book, the second of two volumes, describes the local structure of random graph models for real-world networks and determines when these models have a giant component and when they are small-, and ultra-small, worlds. This is the first book to cover the theory and implications of local convergence, a crucial technique in the analysis of sparse random graphs. Suitable as a resource for researchers and PhD-level courses, it uses examples of real-world networks, such as the Internet and citation networks, as motivation for the models that are discussed, and includes exercises at the end of each chapter to develop intuition. The book closes with an extensive discussion of related models and problems that demonstratemodern approaches to network theory, such as community structure and directed models.
Aviation passenger screening has been used worldwide to mitigate the translocation risk of SARS-CoV-2. We present a model that evaluates factors in screening strategies used in air travel and assess their relative sensitivity and importance in identifying infectious passengers. We use adapted Monte Carlo simulations to produce hypothetical disease timelines for the Omicron variant of SARS-CoV-2 for travelling passengers. Screening strategy factors assessed include having one or two RT-PCR and/or antigen tests prior to departure and/or post-arrival, and quarantine length and compliance upon arrival. One or more post-arrival tests and high quarantine compliance were the most important factors in reducing pathogen translocation. Screening that combines quarantine and post-arrival testing can shorten the length of quarantine for travelers, and variability and mean testing sensitivity in post-arrival RT-PCR and antigen tests decrease and increase with the greater time between the first and second post-arrival test, respectively. This study provides insight into the role various screening strategy factors have in preventing the translocation of infectious diseases and a flexible framework adaptable to other existing or emerging diseases. Such findings may help in public health policy and decision-making in present and future evidence-based practices for passenger screening and pandemic preparedness.
This paper considers semiparametric sieve estimation in high-dimensional single index models. The use of Hermite polynomials in approximating the unknown link function provides a convenient framework to conduct both estimation and variable selection. The estimation of the index parameter is formulated from solutions obtained by the routine penalized weighted linear regression procedure, where the weights are used in order to tackle the unbounded support of the regressors. The resulting index parameter estimator is shown to be consistent and sparse, and the asymptotic normality for the estimators of both the index parameter and the link function is established. To perform variable selection in the ultra-high dimension case, we further suggest a forward regression screening method, which is shown to enjoy the sure independence screening property. This screening procedure can be used before the penalized variable selection to reduce the burden of dimensionality. Numerical results show that both the variable selection procedures and the associated estimators perform well in finite samples.
In this chapter we investigate graph distances in preferential attachment models. We focus on typical distances as well as the diameter of preferential attachment models. We again rely on path-counting techniques, as well as local limit results. Since the local limit is a rather involved quantity, some parts of our analysis are considerably harder than those in Chapters 6 and 7.
In this chapter we investigate the distance structure of the configuration model by investigating its typical distances and its diameter. We adapt the path-counting techniques in Chapter 6 to the configuration model, and obtain typical distances from the “giant is almost local” proof. To understand the ultra-small distances for infinite-variance degree configuration models, we investigate the generation growth of infinite-mean branching processes. The relation to branching processes informally leads to the power-iteration technique that allows one to deduce typical distance results in random graphs in a relatively straightforward way.
In this chapter we investigate the connectivity structure of preferential attachment models. We start by discussing an important tool: exchangeable random variables and their distribution described in de Finetti’s Theorem. We apply these results to Pólya urn schemes, which, in turn, we use to describe the distribution of the degrees in preferential attachment models. It turns out that Pólya urn schemes can also be used to describe the local limit of preferential attachment models. A crucial ingredient is the fact that the edges in the Pólya urn representation are conditionally independent, given the appropriate randomness. The resulting local limit is the Pólya point tree, a specific multi-type branching process with continuous types.
Wastewater-based epidemiology (WBE) has proven to be a powerful tool for the population-level monitoring of pathogens, particularly severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). For assessment, several wastewater sampling regimes and methods of viral concentration have been investigated, mainly targeting SARS-CoV-2. However, the use of passive samplers in near-source environments for a range of viruses in wastewater is still under-investigated. To address this, near-source passive samples were taken at four locations targeting student hall of residence. These were chosen as an exemplar due to their high population density and perceived risk of disease transmission. Viruses investigated were SARS-CoV-2 and its variants of concern (VOCs), influenza viruses, and enteroviruses. Sampling was conducted either in the morning, where passive samplers were in place overnight (17 h) and during the day, with exposure of 7 h. We demonstrated the usefulness of near-source passive sampling for the detection of VOCs using quantitative polymerase chain reaction (qPCR) and next-generation sequencing (NGS). Furthermore, several outbreaks of influenza A and sporadic outbreaks of enteroviruses (some associated with enterovirus D68 and coxsackieviruses) were identified among the resident student population, providing evidence of the usefulness of near-source, in-sewer sampling for monitoring the health of high population density communities.
Extreme precipitation events are occurring more intensely in Canada. This can contaminate water sources with enteric pathogens, potentially increasing the risk of acute gastrointestinal illness. This study aimed to investigate the relationship between extreme precipitation and emergency department (ED) visits for acute gastrointestinal illness in Toronto from 2012 to 2022. Distributed lag non-linear models were constructed on ED visit counts with a Quasi Poisson distribution. Extreme precipitation was modelled as a 21-day lag variable, with a linear relationship assumed at levels ≧95th percentile. Separate models were also conducted on season-specific data sets. Daily precipitation and gastrointestinal illness ED visits ranged between 0 to 126 mm, and 12 to 180 visits respectively. Overall, a 10-mm increase in precipitation >95th percentile had no significant relationship with the risk of ED visits. However, stratification by seasons revealed significant relationships during spring (lags 1–19, peak at lag 14 RR = 1.04; 95% CI: 1.03, 1.06); the overall cumulative effect across the 21-day lag was also significant (RR = 1.94; 95% CI: 1.47, 2.57). Extreme precipitation has a seasonal effect on gastrointestinal health outcomes in Toronto city, suggesting varying levels of enteric pathogen exposures through drinking water or other environmental pathway during different seasons.
In this chapter we draw motivation from real-world networks and formulate random graph models for them. We focus on some of the models that have received the most attention in the literature, namely, Erdos–Rényi random graphs, inhomogeneous random graphs, configuration models, and preferential attachment models. We follow Volume 1, both for the motivation as well as for the introduction of the random graph models involved. Furthermore, we add some convenient additional results, such as degree-truncation for configuration models and switching techniques for uniform random graphs with prescribed degrees. We also discuss preliminaries used in the book, for example concerning power-law distributions.