The financing of long-term care and the planning of care capacity are of increasing interest due to demographic changes and the ageing population in many countries. Since many care-intensive conditions begin to manifest at higher ages, a better understanding and assessment of the expected costs, required infrastructure, and number of qualified personnel are essential. To evaluate the overall burden of institutional care, we derive a model based on the duration of stay in dependence and the intensity of help provided to elderly individuals. This article aims to model both aspects using novel longitudinal data from nursing homes in the canton of Geneva in Switzerland. Our data contain comprehensive health and care information, including medical diagnoses, levels of dependence, and physical and psychological impairments on 21,758 individuals. We build an accelerated failure time model to study the influence of selected factors on the duration of care and a beta regression model to describe the intensity of care. We show that apart from age and gender, the duration of stay before death is mainly affected by the underlying diseases and the number of different diagnoses. Simultaneously, care intensity is driven by the individual level of dependence and specific limitations. Using both evaluations, we approximate the overall care severity for individual profiles. Our study sheds light on the relevant medical, physical, and psychological health indicators that need to be accounted for, not only by care providers but also by policy-makers and insurers.

Let $q\ge2$ be an integer, $\{X_n\}_{n\geq 1}$ a stochastic process with state space $\{0,\ldots,q-1\}$, and F the cumulative distribution function (CDF) of $\sum_{n=1}^\infty X_n q^{-n}$. We show that stationarity of $\{X_n\}_{n\geq 1}$ is equivalent to a functional equation obeyed by F, and use this to characterize the characteristic function of X and the structure of F in terms of its Lebesgue decomposition. More precisely, while the absolutely continuous component of F can only be the uniform distribution on the unit interval, its discrete component can only be a countable convex combination of certain explicitly computable CDFs for probability distributions with finite support. We also show that $\mathrm{d} F$ is a Rajchman measure if and only if F is the uniform CDF on [0, 1].

Statistical learning—the skill to pick up probability-based regularities of the environment—plays a crucial role in adapting to the environment and learning perceptual, motor, and language skills in healthy and clinical populations. Here, we developed a new method to measure statistical learning without any manual responses. We used the Alternating Serial Reaction Time (ASRT) task, adapted to eye-tracker, which, besides measuring reaction times (RTs), enabled us to track learning-dependent anticipatory eye movements. We found robust, interference-resistant learning on RT; moreover, learning-dependent anticipatory eye movements were even more sensitive measures of statistical learning on this task. Our method provides a way to apply the widely used ASRT task to operationalize statistical learning in clinical populations where the use of manual tasks is hindered, such as in Parkinson’s disease. Furthermore, it also enables future basic research to use a more sensitive version of this task to measure predictive processing.

In this paper, we extend the optimal dividend and capital injection problem with affine penalty at ruin in (Xu, R. & Woo, J.K. (2020). Insurance: Mathematics and Economics 92: 1–16) to the case with singular dividend payments. The asymptotic relationships between our value function to the one with bounded dividend density are studied, which also help to verify that our value function is a viscosity solution to the associated Hamilton–Jacob–Bellman Quasi-Variational Inequality (HJBQVI). We also show that the value function is the smallest viscosity supersolution within certain functional class. A modified comparison principle is proved to guarantee the uniqueness of the value function as the viscosity solution within the same functional class. Finally, a band-type dividend and capital injection strategy is constructed based on four crucial sets; and the optimality of such band-type strategy is proved by using fixed point argument. Numerical examples of the optimal band-type strategies are provided at the end when the claim size follows exponential and gamma distribution, respectively.

Almost stochastic dominance has been receiving a great amount of attention in the financial and economic literatures. In this paper, we characterize the properties of almost first-order stochastic dominance (AFSD) via distorted expectations and investigate the conditions under which AFSD is preserved under a distortion transform. The main results are also applied to establish stochastic comparisons of order statistics and receiver operating characteristic curves via AFSD.

We recently described a simple model through which we assessed what effect subjecting travellers to a single on-arrival test might have on reducing risk of importing disease cases during simulated outbreaks of coronavirus disease 2019 (COVID-19), influenza, severe acute respiratory syndrome (SARS) and Ebola. We build upon this work to allow for the additional requirement that inbound travellers also undergo a period of self-isolation upon arrival, where upon completion the traveller is again tested for signs of infection prior to admission across the border. Prior results indicated that a single on-arrival test has the potential to detect 9% of travellers infected with COVID-19, compared to 35%, 10% and 3% for travellers infected with influenza, SARS and Ebola, respectively. Our extended model shows that testing administered after a 2-day isolation period could detect up to 41%, 97%, 44% and 15% of COVID-19, influenza, SARS and Ebola infected travellers, respectively. Longer self-isolation periods increase detection rates further, with an 8-day self-isolation period suggesting detection rates of up to 94%, 100%, 98% and 62% for travellers infected with COVID-19, influenza, SARS and Ebola, respectively. These results therefore suggest that testing arrivals after an enforced period of self-isolation may present a reasonable method of protecting against case importation during international outbreaks.

We study the quasi-stationary behavior of the birth–death process with an entrance boundary at infinity. We give by the h-transform an alternative and simpler proof for the exponential convergence of conditioned distributions to a unique quasi-stationary distribution in the total variation norm. In addition, we also show that starting from any initial distribution the conditional probability converges to the unique quasi-stationary distribution exponentially fast in the $\psi$-norm.

We examined the possible sex and age differences in the proportion of experienced Coronavirus Disease 2019 (COVID-19) symptoms in unaware (previously) infected adults, and their uninfected counterparts, estimated by serostatus prior to vaccination, at the end of 2020 (Wuhan strain). A cross-sectional community-based study using a convenience sample of 10 001 adult inhabitants of a southern Dutch province, heavily affected by COVID-19, was conducted. Participants donated a blood sample to indicate past infection by serostatus (positive/negative). Experienced symptoms were assessed by questionnaire, before the availability of the serological test result. Only participants without confirmed SARS-CoV-2 infection were included (n = 9715, age range 18–90 years). The seroprevalence was comparable between men (17.3%) and women (18.0%), and participants aged 18–60 years (17.3%) and aged 60 years and older (18.6%). We showed sex and age differences in the proportion experienced symptoms by serostatus in a large cohort of both unaware (untested) seropositive compared with seronegative reference participants. Irritability only differed by serostatus in men (independent of age), while stomach ache, nausea and dizziness only differed by serostatus in women aged 60 years and older. Besides, the proportion of experiencing pain when breathing and headache differed by serostatus in men aged 18–60 years only. Our study highlights the importance of taking possible sex and age differences into account with respect to acute and long-term COVID-19 outcomes. Identifying symptom profiles for sex and age subgroups can contribute to timely identification of infection, gaining importance once governments currently move away from mass testing again.

Population-based structural health monitoring (PBSHM) provides a means of accounting for inter-turbine correlations when solving the problem of wind farm anomaly detection. Across a wind farm, where a group of structures (turbines) is placed in close vicinity to each other, the environmental conditions and, thus, structural behavior vary in a spatiotemporal manner. Spatiotemporal trends are often overlooked in the existing data-based wind farm anomaly detection methods, because most current methods are designed for individual structures, that is, detecting anomalous behavior of a turbine based on the past behavior of the same turbine. In contrast, the idea of PBSHM involves sharing data across a population of structures and capturing the interactions between structures. This paper proposes a population-based anomaly detection method, specifically for a localized population of structures, which accounts for the spatiotemporal correlations in structural behavior. A case study from an offshore wind farm is given to demonstrate the potential of the proposed method as a wind farm performance indicator. It is concluded that the method has the potential to indicate operational anomalies caused by a range of factors across a wind farm. The method may also be useful for other tasks such as wind power and turbine load modeling.

It is well known that each statistic in the family of power divergence statistics, across n trials and r classifications with index parameter $\lambda\in\mathbb{R}$ (the Pearson, likelihood ratio, and Freeman–Tukey statistics correspond to $\lambda=1,0,-1/2$, respectively), is asymptotically chi-square distributed as the sample size tends to infinity. We obtain explicit bounds on this distributional approximation, measured using smooth test functions, that hold for a given finite sample n, and all index parameters ($\lambda>-1$) for which such finite-sample bounds are meaningful. We obtain bounds that are of the optimal order $n^{-1}$. The dependence of our bounds on the index parameter $\lambda$ and the cell classification probabilities is also optimal, and the dependence on the number of cells is also respectable. Our bounds generalise, complement, and improve on recent results from the literature.

We analyse features of the patterns formed from a simple model for a martensitic phase transition that fragments the unit square into rectangles. This is a fragmentation model that can be encoded by a general branching random walk. An important quantity is the distribution of the lengths of the interfaces in the pattern, and we establish limit theorems for some of the asymptotics of the interface profile. In particular, we are able to use a general branching process to show almost sure power law decay of the number of interfaces of at least a certain size and a general branching random walk to examine the numbers of rectangles of a certain aspect ratio. In doing so we extend a theorem on the growth of the general branching random walk as well as developing results on the tail behaviour of the limiting random variable in our general branching process.

We study convergence to non-minimal quasi-stationary distributions for one-dimensional diffusions. We give a method for reducing the convergence to the tail behavior of the lifetime via a property we call the first hitting uniqueness. We apply the results to Kummer diffusions with negative drift and give a class of initial distributions converging to each non-minimal quasi-stationary distribution.

In this article, we explore the challenges of global governance and the particular challenge presented by global data governance. We discuss a range of challenges to developing meaningful global governance institutions for regulating how companies and governments around the world manage and utilize consumer data. These challenges are compounded by their global nature and the complexities of Internet-based technologies. We argue that the following gaps exist for effective global data governance: (a) there is no overarching global framework for protecting consumer data, and it is partial and incomplete; (b) there is a lack of data protection for international data transfers, as much of the regulation that is being developed is not global in scale; and (c) new areas of data collection and use compound concerns to effective data governance in a globalized digital world. Moreover, we highlight important needs in terms of both global governance and impending challenges related to current and new uses of data. Any global governance framework should recognize the need for an iterative process where communication is ongoing between the necessary stakeholders. Agreements should incorporate common goals to maximize the potential development of global data governance norms. However, goals must remain flexible to the different data environments across nation-states while maintaining a global scope to ensure data protection. In addition, any agreement should consider the emerging challenges in this area. These challenges include new methods of data collection and use, as well as protecting individuals from manipulation and undue influence based on how their data are being used, processed, and collected.

We show that load-sharing models (a very special class of multivariate probability models for nonnegative random variables) can be used to obtain basic results about a multivariate extension of stochastic precedence and related paradoxes. Such results can be applied in several different fields. In particular, applications of them can be developed in the context of paradoxes which arise in voting theory. Also, an application to the notion of probability signature may be of interest, in the field of systems reliability.

In March 2018, the US Food and Drug Administration (FDA), US Centers for Disease Control and Prevention, California Department of Public Health, Los Angeles County Department of Public Health and Pennsylvania Department of Health initiated an investigation of an outbreak of Burkholderia cepacia complex (Bcc) infections. Sixty infections were identified in California, New Jersey, Pennsylvania, Maine, Nevada and Ohio. The infections were linked to a no-rinse cleansing foam product (NRCFP), produced by Manufacturer A, used for skin care of patients in healthcare settings. FDA inspected Manufacturer A's production facility (manufacturing site of over-the-counter drugs and cosmetics), reviewed production records and collected product and environmental samples for analysis. FDA's inspection found poor manufacturing practices. Analysis by pulsed-field gel electrophoresis confirmed a match between NRCFP samples and clinical isolates. Manufacturer A conducted extensive recalls, FDA issued a warning letter citing the manufacturer's inadequate manufacturing practices, and federal, state and local partners issued public communications to advise patients, pharmacies, other healthcare providers and healthcare facilities to stop using the recalled NRCFP. This investigation highlighted the importance of following appropriate manufacturing practices to minimize microbial contamination of cosmetic products, especially if intended for use in healthcare settings.

Branching-stable processes have recently appeared as counterparts of stable subordinators, when addition of real variables is replaced by branching mechanisms for point processes. Here we are interested in their domains of attraction and describe explicit conditions for a branching random walk to converge after a proper magnification to a branching-stable process. This contrasts with deep results obtained during the past decade on the asymptotic behavior of branching random walks and which involve either shifting without rescaling, or demagnification.

This paper studies the properties of predictive regressions for asset returns in economic systems governed by persistent vector autoregressive dynamics. In particular, we allow for the state variables to be fractionally integrated, potentially of different orders, and for the returns to have a latent persistent conditional mean, whose memory is difficult to estimate consistently by standard techniques in finite samples. Moreover, the predictors may be endogenous and “imperfect.” In this setting, we develop a consistent local spectrum (LCM) estimation procedure, that delivers asymptotic Gaussian inference. Furthermore, we provide a new LCM-based estimator of the conditional mean persistence, that leverages biased regression slopes as well as new LCM-based tests for significance of (a subset of) the predictors, which are valid even without estimating the return persistence. Simulations illustrate the theoretical arguments. Finally, an empirical application to monthly S&P 500 return predictions provides evidence for a fractionally integrated conditional mean component. Our new LCM procedure and tools indicate significant predictive power for future returns stemming from key state variables such as the default spread and treasury interest rates.

Conditional value-at-risk (CVaR) and conditional expected shortfall (CES) are widely adopted risk measures which help monitor potential tail risk while adapting to evolving market information. In this paper, we propose an approach to constructing simultaneous confidence bands (SCBs) for tail risk as measured by CVaR and CES, with the confidence bands uniformly valid for a set of tail levels. We consider one-sided tail risk (downside or upside tail risk) as well as relative tail risk (the ratio of upside to downside tail risk). A general class of location-scale models with heavy-tailed innovations is employed to filter out the return dynamics. Then, CVaR and CES are estimated with the aid of extreme value theory. In the asymptotic theory, we consider two scenarios: (i) the extreme scenario that allows for extrapolation beyond the range of the available data and (ii) the intermediate scenario that works exclusively in the case where the available data are adequate relative to the tail level. For finite-sample implementation, we propose a novel bootstrap procedure to circumvent the slow convergence rates of the SCBs as well as infeasibility of approximating the limiting distributions. A series of Monte Carlo simulations confirm that our approach works well in finite samples.