We consider a class of phase-type distributions (PH-distributions), to be called the MMPP class of PH-distributions, and find bounds of their mean and squared coefficient of variation (SCV). As an application, we have shown that the SCV of the event-stationary inter-event time for Markov modulated Poisson processes (MMPPs) is greater than or equal to unity, which answers an open problem for MMPPs. The results are useful for selecting proper PH-distributions and counting processes in stochastic modeling.

In a multitype branching process, it is assumed that immigrants arrive according to a non-homogeneous Poisson or a contagious Poisson process (both processes are formulated as a non-homogeneous birth process with an appropriate choice of transition intensities). We show that the normalized numbers of objects of the various types alive at time t for supercritical, critical, and subcritical cases jointly converge in distribution under those two different arrival processes. Furthermore, we provide some transient expectation results when there are only two types of particles.

Motivated by applications to a wide range of areas, including assemble-to-order systems, operations scheduling, healthcare systems, and the collaborative economy, we study a stochastic matching model on hypergraphs, extending the model of Mairesse and Moyal (J. Appl. Prob. 53, 2016) to the case of hypergraphical (rather than graphical) matching structures. We address a discrete-event system under a random input of single items, simply using the system as an interface to be matched in groups of two or more. We primarily study the stability of this model, for various hypergraph geometries.

This study investigated the effects of pretreatment with antioxidants, kaempferol, and zinc gluconate on serum biochemical changes and impairment in body weight gain following noise-exposure in Wistar rats. Thirty-five animals were evenly grouped into five cohorts: Groups II, III, IV, and V were exposed to noise stress, induced by exposing rats to 100 dB (4 hr/day) for 15 days, from days 33 to 48 after starting the drug treatments. Treatment with kaempferol and/or zinc mitigated noise-induced deficits in body weight gain, and levels of serum lipid and protein fractions. The combined treatment significantly (p < .05) decreased malondialdehyde concentration in kaempferol + zinc gluconate treated group, compared to the group administered deionized water + noise. This result demonstrates that biochemical dyshomeostasis and lipid peroxidation may be involved in the molecular mechanism underlying noise stress and the assortment of kaempferol and zinc gluconate produced an improved mitigating outcome in Wistar rats.

In addition to the features of the two-parameter Chinese restaurant process (CRP), the restaurant under consideration has a cocktail bar and hence allows for a wider range of (bar and table) occupancy mechanisms. The model depends on three real parameters, $\alpha$, $\theta_1$, and $\theta_2$, fulfilling certain conditions. Results known for the two-parameter CRP are carried over to this model. We study the number of customers at the cocktail bar, the number of customers at each table, and the number of occupied tables after n customers have entered the restaurant. For $\alpha>0$ the number of occupied tables, properly scaled, is asymptotically three-parameter Mittag–Leffler distributed as n tends to infinity. We provide representations for the two- and three-parameter Mittag–Leffler distribution leading to efficient random number generators for these distributions. The proofs draw heavily from methods known for exchangeable random partitions, martingale methods known for generalized Pólya urns, and results known for the two-parameter CRP.

Regular variation provides a convenient theoretical framework for studying large events. In the multivariate setting, the spectral measure characterizes the dependence structure of the extremes. This measure gathers information on the localization of extreme events and often has sparse support since severe events do not simultaneously occur in all directions. However, it is defined through weak convergence, which does not provide a natural way to capture this sparsity structure. In this paper, we introduce the notion of sparse regular variation, which makes it possible to better learn the dependence structure of extreme events. This concept is based on the Euclidean projection onto the simplex, for which efficient algorithms are known. We prove that under mild assumptions sparse regular variation and regular variation are equivalent notions, and we establish several results for sparsely regularly varying random vectors.

A common tool in the practice of Markov chain Monte Carlo (MCMC) is to use approximating transition kernels to speed up computation when the desired kernel is slow to evaluate or is intractable. A limited set of quantitative tools exists to assess the relative accuracy and efficiency of such approximations. We derive a set of tools for such analysis based on the Hilbert space generated by the stationary distribution we intend to sample, $L_2(\pi)$. Our results apply to approximations of reversible chains which are geometrically ergodic, as is typically the case for applications to MCMC. The focus of our work is on determining whether the approximating kernel will preserve the geometric ergodicity of the exact chain, and whether the approximating stationary distribution will be close to the original stationary distribution. For reversible chains, our results extend the results of Johndrow et al. (2015) from the uniformly ergodic case to the geometrically ergodic case, under some additional regularity conditions. We then apply our results to a number of approximate MCMC algorithms.

We prove concentration inequality results for geometric graph properties of an instance of the Cooper–Frieze [5] preferential attachment model with edge-steps. More precisely, we investigate a random graph model that at each time $t\in \mathbb{N}$, with probability p adds a new vertex to the graph (a vertex-step occurs) or with probability $1-p$ an edge connecting two existent vertices is added (an edge-step occurs). We prove concentration results for the global clustering coefficient as well as the clique number. More formally, we prove that the global clustering, with high probability, decays as $t^{-\gamma(p)}$ for a positive function $\gamma$ of p, whereas the clique number of these graphs is, up to subpolynomially small factors, of order $t^{(1-p)/(2-p)}$.

In the collector’s problem with group drawings, s out of n different types of coupon are sampled with replacement. In the uniform case, each s-subset of the types has the same probability of being sampled. For this case, we derive a Poisson limit theorem for the number of types that are sampled at most $c-1$ times, where $c \ge 1$ is fixed. In a specified approximate nonuniform setting, we prove a Poisson limit theorem for the special case $c=1$. As corollaries, we obtain limit distributions for the waiting time for c complete series of types in the uniform case and a single complete series in the approximate nonuniform case.

We study shot noise processes with cluster arrivals, in which entities in each cluster may experience random delays (possibly correlated), and noises within each cluster may be correlated. We prove functional limit theorems for the process in the large-intensity asymptotic regime, where the arrival rate gets large while the shot shape function, cluster sizes, delays, and noises are unscaled. In the functional central limit theorem, the limit process is a continuous Gaussian process (assuming the arrival process satisfies a functional central limit theorem with a Brownian motion limit). We discuss the impact of the dependence among the random delays and among the noises within each cluster using several examples of dependent structures. We also study infinite-server queues with cluster/batch arrivals where customers in each batch may experience random delays before receiving service, with similar dependence structures.

Under a fourth-order moment condition on the branching and a second-order moment condition on the immigration mechanisms, we show that an appropriately scaled projection of a supercritical and irreducible continuous-state and continuous-time branching process with immigration on certain left non-Perron eigenvectors of the branching mean matrix is asymptotically mixed normal. With an appropriate random scaling, under some conditional probability measure, we prove asymptotic normality as well. In the case of a non-trivial process, under a first-order moment condition on the immigration mechanism, we also prove the convergence of the relative frequencies of distinct types of individuals on a suitable event; for instance, if the immigration mechanism does not vanish, then this convergence holds almost surely.

Parametric mortality models permit detailed analysis of risk factors for actuarial work. However, finite data volumes lead to uncertainty over parameter estimates, which in turn gives rise to mis-estimation risk of financial liabilities. Mis-estimation risk can be assessed on a run-off basis by valuing the liabilities with alternative parameter vectors consistent with the covariance matrix. This run-off approach is especially suitable for tasks like pricing portfolio transactions, such as bulk annuities, longevity swaps or reinsurance treaties. However, a run-off approach does not fully meet the requirements of regulatory regimes that view capital requirements through the prism of a finite horizon, such as Solvency II’s one-year approach. This paper presents a methodology for viewing mis-estimation risk over a fixed time frame, and results are given for a specimen portfolio. As expected, we find that time-limited mis-estimation capital requirements increase as the horizon is lengthened or the discount rate is reduced. However, we find that much of the so-called mis-estimation risk in a one-year value-at-risk assessment can actually be driven by idiosyncratic variation, rather than parameter uncertainty. This counter-intuitive result stems from trying to view a long-term risk through a short-term window. As a result, value-at-risk mis-estimation reserves are strongly correlated with idiosyncratic risk. We also find that parsimonious models tend to produce lower mis-estimation risk than less-parsimonious ones.

The aim of our study was to determine the distribution of hepatitis B virus (HBV) genotypes and subgenotypes in ethnic minorities in Yunnan province to provide evidence supporting the theoretical basis for hepatitis B prevention and control. We obtained serum samples and demographic data from 765 individuals reported by Yunnan province who had either acute or chronic HBV infection and were from one of 20 ethnic minority populations: Achang, Bai, Brown, Tibetan, Dai, Deang, Dulong, Hani, Hui, Jingpo, Lahu, Yi, Lisu Miao, Naxi, Nu, Pumi, Wa, Yao, or Zhuang people. We sequenced the HBV DNA and determined the genotypes and subgenotypes of the isolated HBVs. We mapped the genotype and subgenotype distribution by ethnic minority population and conducted descriptive analyses. There were four genotypes among the 20 ethnic groups: genotype B (21.3% of samples), C (76.6%), D (1.8%) and I (0.3%). The most common subgenotype was C1. There were no genotype differences by gender (P = 0.954) or age (P = 0.274), but there were differences by region (P < 0.001). There were differences in genotype distribution (P < 0.001) and subgenotype distribution (P = 0.011) by ethnic group. Genotype D was most prominent in Tibet and most HBV isolates were C/D recombinant viruses. The only two genotype I virus isolates were in Zhuang people. Susceptibility and geographic patterns may influence HBV prevalence in different ethnic populations, but additional research is needed for such a determination.

This paper highlights the need and opportunities for constructively combining different types of (analogue and data-driven) knowledges in evidence-informed policy decision-making in future smart cities. Problematizing the assumed universality and objectivity of data-driven knowledge, we call attention to notions of “positionality” and “situatedness” in knowledge production relating to the urban present and possible futures. In order to illustrate our arguments, we draw on a case study of strategic urban (spatial) planning in the Cambridge city region in the United Kingdom. Tracing diverse knowledge production processes, including top-down data-driven knowledges derived from urban modeling, and bottom-up analogue community-based knowledges, allows us to identify locationally specific knowledge politics around evidence for policy. The findings highlight how evidence-informed urban policy can benefit from political processes of competition, contestation, negotiation, and complementarity that arise from interactions between diverse “digital” and “analogue” knowledges. We argue that studying such processes can help in assembling a more multifaceted, diverse and inclusive knowledge-base on which to base policy decisions, as well as to raise awareness and improve active participation in the ongoing “smartification” of cities.

This paper introduces a novel wild bootstrap for dependent data (WBDD) as a means of calculating standard errors of estimators and constructing confidence regions for parameters based on dependent heterogeneous data. The consistency of the bootstrap variance estimator for smooth function of the sample mean is shown to be robust against heteroskedasticity and dependence of unknown form. The first-order asymptotic validity of the WBDD in distribution approximation is established when data are assumed to satisfy a near epoch dependent condition and under the framework of the smooth function model. The WBDD offers a viable alternative to the existing non parametric bootstrap methods for dependent data. It preserves the second-order correctness property of blockwise bootstrap (provided we choose the external random variables appropriately), for stationary time series and smooth functions of the mean. This desirable property of any bootstrap method is not known for extant wild-based bootstrap methods for dependent data. Simulation studies illustrate the finite-sample performance of the WBDD.

Identification of societal activities associated with SARS-CoV-2 infection may provide an evidence base for implementing preventive measures. Here, we investigated potential determinants for infection in Denmark in a situation where society was only partially open. We conducted a national matched case-control study. Cases were recent RT-PCR test-positives, while controls, individually matched on age, sex and residence, had not previously tested positive for SARS-CoV-2. Questions concerned person contact and community exposures. Telephone interviews were performed over a 7-day period in December 2020. We included 300 cases and 317 controls and determined odds ratios (ORs) and 95% confidence intervals (95% CI) by conditional logistical regression with adjustment for household size and country of origin. Contact (OR 4.9, 95% CI 2.4–10) and close contact (OR 13, 95% CI 6.7–25) with a person with a known SARS-CoV-2 infection were main determinants. Contact most often took place in the household or work place. Community determinants included events with singing (OR 2.1, 95% CI 1.1–4.1), attending fitness centres (OR 1.8, 95% CI 1.1–2.8) and consumption of alcohol in a bar (OR 10, 95% CI 1.5–65). Other community exposures appeared not to be associated with infection, these included shopping at supermarkets, travel by public transport, dining at restaurants and private social events with few participants. Overall, the restrictions in place at the time of the study appeared to be sufficient to reduce transmission of disease in the public space, which instead largely took place following direct exposures to people with known SARS-CoV-2 infections.