The paper is concerned with common shock models of claim triangles. These are usually constructed as linear combinations of shock components and idiosyncratic components. Previous literature has discussed the unbalanced property of such models, whereby the shocks may over- or under-contribute to some observations. The literature has also introduced corrections for this. The present paper discusses “auto-balanced” models, in which all shock and idiosyncratic components contribute to observations such that their proportionate contributions are constant from one observation to another. The conditions for auto-balance are found to be simple and applicable to a wide range of model structures. Numerical illustrations are given.

An extension of Shannon’s entropy power inequality when one of the summands is Gaussian was provided by Costa in 1985, known as Costa’s concavity inequality. We consider the additive Gaussian noise channel with a more realistic assumption, i.e. the input and noise components are not independent and their dependence structure follows the well-known multivariate Gaussian copula. Two generalizations for the first- and second-order derivatives of the differential entropy of the output signal for dependent multivariate random variables are derived. It is shown that some previous results in the literature are particular versions of our results. Using these derivatives, concavity of the entropy power, under certain mild conditions, is proved. Finally, special one-dimensional versions of our general results are described which indeed reveal an extension of the one-dimensional case of Costa’s concavity inequality to the dependent case. An illustrative example is also presented.

Two ensembles are frequently used to model random graphs subject to constraints: the microcanonical ensemble (= hard constraint) and the canonical ensemble (= soft constraint). It is said that breaking of ensemble equivalence (BEE) occurs when the specific relative entropy of the two ensembles does not vanish as the size of the graph tends to infinity. Various examples have been analysed in the literature. It was found that BEE is the rule rather than the exception for two classes of constraints: sparse random graphs when the number of constraints is of the order of the number of vertices, and dense random graphs when there are two or more constraints that are frustrated. We establish BEE for a third class: dense random graphs with a single constraint on the density of a given simple graph. We show that BEE occurs in a certain range of choices for the density and the number of edges of the simple graph, which we refer to as the BEE-phase. We also show that, in part of the BEE-phase, there is a gap between the scaling limits of the averages of the maximal eigenvalue of the adjacency matrix of the random graph under the two ensembles, a property that is referred to as the spectral signature of BEE. We further show that in the replica symmetric region of the BEE-phase, BEE is due to the coexistence of two densities in the canonical ensemble.

We consider a premium control problem in discrete time, formulated in terms of a Markov decision process. In a simplified setting, the optimal premium rule can be derived with dynamic programming methods. However, these classical methods are not feasible in a more realistic setting due to the dimension of the state space and lack of explicit expressions for transition probabilities. We explore reinforcement learning techniques, using function approximation, to solve the premium control problem for realistic stochastic models. We illustrate the appropriateness of the approximate optimal premium rule compared with the true optimal premium rule in a simplified setting and further demonstrate that the approximate optimal premium rule outperforms benchmark rules in more realistic settings where classical approaches fail.

In this study, we quantify the relationship between socio-economic status and life expectancy and identify combinations of socio-economic variables that are particularly useful for explaining mortality differences between neighbourhoods in England. We achieve this by examining socio-economic variation in mortality experiences across small areas in England known as lower layer super output areas (LSOAs). We then consider 12 socio-economic variables that are known to have a strong association with mortality. We estimate the relationship between those variables and mortality rates using a random forest algorithm. Based on the resulting estimate, we then create a new socio-economic mortality index – the Longevity Index for England (LIFE). The index is constructed in a way that eliminates the impact of care homes that might artificially increase mortality rates in LSOAs with care homes compared to LSOAs that do not contain a care home. Using mortality data for different age groups, we make the index age-dependent and investigate the impact of specific socio-economic characteristics on the age-specific mortality risk. We compare the explanatory power of the LIFE index to the English Index of Multiple Deprivation (IMD) as predictors of mortality. While we find that the IMD can explain regional mortality differences to some extent, the LIFE index has significantly greater explanatory power for mortality differences between regions. Our empirical results also indicate that income deprivation amongst the elderly and employment deprivation are the most significant socio-economic factors for explaining mortality variation across LSOAs in England.

Stein’s method is used to study discrete representations of multidimensional distributions that arise as approximations of states of quantum harmonic oscillators. These representations model how quantum effects result from the interaction of finitely many classical ‘worlds’, with the role of sample size played by the number of worlds. Each approximation arises as the ground state of a Hamiltonian involving a particular interworld potential function. Our approach, framed in terms of spherical coordinates, provides the rate of convergence of the discrete approximation to the ground state in terms of Wasserstein distance. Applying a novel Stein’s method technique to the radial component of the ground state solution, the fastest rate of convergence to the ground state is found to occur in three dimensions.

We explored the feasibility, suitability, and reliability of using controls recruited among members of a non-probabilistic online panel (‘panel controls’) in a case–control study (CCS) to investigate a Salmonella Braenderup outbreak in Germany. For comparison, another control group was recruited via random digit dialling (‘classical controls’). Panel members received questionnaires by email; classical controls were interviewed by phone. Both control groups were frequency-matched to cases by age and sex; the classical controls also by federal state. Cases and controls were queried mainly about fruit consumption since melons were the suspected infection vehicle. We calculated adjusted odds ratios (aOR) and 95% confidence intervals (CIs) using single-variable and multivariable logistic regression. The study included 32 cases, 81 panel controls and 110 classical controls. Analyses identified melons, particularly Galia melons, as the most likely infection vehicle using either control group (panel controls – aOR 12, CI 2.7–66; classical controls – aOR 55, CI 8–1100). Recruitment of panel versus classical controls required substantially less person-time (8 vs. 111 hours) and was about 10 times less expensive. We recommend this timely and reliable control recruitment method when investigating diffuse foodborne outbreaks with CCS.

In relational event networks, endogenous statistics are used to summarize the past activity between actors. Typically, it is assumed that past events have equal weight on the social interaction rate in the (near) future regardless of the time that has transpired since observing them. Generally, it is unrealistic to assume that recently past events affect the current event rate to an equal degree as long-past events. Alternatively one may consider using a prespecified decay function with a prespecified rate of decay. A problem then is that the chosen decay function could be misspecified yielding biased results and incorrect conclusions. In this paper, we introduce three parametric weight decay functions (exponential, linear, and one-step) that can be embedded in a relational event model. A statistical method is presented to decide which memory decay function and memory parameter best fit the observed sequence of events. We present simulation studies that show the presence of bias in the estimates of effects of the statistics whenever the decay, as well as the memory parameter, are not properly estimated, and the ability to test different memory models against each other using the Bayes factor. Finally, we apply the methodology to two empirical case studies.

In this paper, we establish some stochastic comparison results for largest claim amounts of two sets of independent and also for interdependent portfolios under the setup of the proportional odds model. We also establish stochastic comparison results for aggregate claim amounts of two sets of independent portfolios. Further, stochastic comparisons for largest claim amounts from two sets of independent multiple-outlier claims have also been studied. The results we obtained apply to the whole family of extended distributions, also known as the Marshall–Olkin family of distributions. We have given many numerical examples to illustrate the results obtained.

Few prospective studies have documented the seropositivity among those children infected with severe acute respiratory syndrome coronavirus 2. From 2 April 2021 to 24 June 2021, we prospectively enrolled children between the ages of 2 and 17 years at three North Carolina healthcare systems. Participants received at least four at-home serological tests detecting the presence of antibodies against, but not differentiating between, the nucleocapsid or spike antigen. A total of 1,058 participants were enrolled in the study, completing 2,709 tests between 1 May 2021 and 31 October 2021. Using multilevel regression with poststratification techniques and considering our assay sensitivity and sensitivity, we estimated that the seroprevalence of infection-induced antibodies among unvaccinated children and adolescents aged 2–17 years in North Carolina increased from 15.2% (95% credible interval, CrI 9.0–22.0) in May 2021 to 54.1% (95% CrI 46.7–61.1) by October 2021, indicating an average infection-to-reported-case ratio of 5. A rapid rise in seropositivity was most pronounced in those unvaccinated children aged 12–17 years, based on our estimates. This study underlines the utility of serial, serological testing to inform a broader understanding of the regional immune landscape and spread of infection.

Healthcare workers’ (HCWs) safety and availability to care for patients are critical during a pandemic such as the one caused by severe acute respiratory syndrome coronavirus 2. Among providers of different specialities, it is critical to protect those working in hospital settings with a high risk of infection. Using an agent-based simulation model, various staffing policies were developed and simulated for 90 days using data from the largest health systems in South Carolina. The model considers staffing policies that include geographic segregation, interpersonal contact limits, and a combination of factors, including the patient census, transmission rates, vaccination status of providers, hospital capacity, incubation time, quarantine period, and interactions between patients and providers. Comparing the existing practices to various risk-adjusted staffing policies, model predictions show that restricted teaming and rotating schedules significantly (p-value <0.01) reduced weekly HCW unavailability and the number of infected HCWs by 22% and 38%, respectively, when the vaccination rates among HCWs were lower (<75%). However, as the vaccination rate increases, the benefits of risk-adjusted policies diminish; and when 90% of HCWs were vaccinated, there were no significant (p-value = 0.09) benefits. Although these simulated outcomes are specific to one health system, our findings can be generalised to other health systems with multiple locations.

Approximately 80 million people live with chronic hepatitis B virus (HBV) infection in the WHO Africa Region. The natural history of HBV infection in this population is poorly characterised, and may differ from patterns observed elsewhere due to differences in prevailing genotypes, environmental exposures, co-infections, and host genetics. Existing research is largely drawn from small, single-centre cohorts, with limited follow-up time. The Hepatitis B in Africa Collaborative Network (HEPSANET) was established in 2022 to harmonise the process of ongoing data collection, analysis, and dissemination from 13 collaborating HBV cohorts in eight African countries. Research priorities for the next 5 years were agreed upon through a modified Delphi survey prior to baseline data analysis being conducted. Baseline data on 4,173 participants with chronic HBV mono-infection were collected, of whom 38.3% were women and the median age was 34 years (interquartile range 28–42). In total, 81.3% of cases were identified through testing of asymptomatic individuals. HBeAg-positivity was seen in 9.6% of participants. Follow-up of HEPSANET participants will generate evidence to improve the diagnosis and management of HBV in this region.

The survival energy model (SEM) is a recently introduced novel approach to mortality prediction, which offers a cohort-wise distribution function of the time of death as the first hitting time of a “survival energy” diffusion process to zero. In this study, we propose a novel SEM that can serve as a suitable candidate in the family of prediction models. We also proposed a method to improve the prediction in an earlier work. We further examine the practical advantages of SEM over existing mortality models.

Oesophageal cancer is the most common gastrointestinal malignancy in China and one of the major causes of death due to cancer worldwide. The occurrence of oesophageal cancer is a multifactor, multistage, and multistep process influenced by heredity, the environment, and microorganisms. Specifically, bacterial infection may be involved in the process of tissue carcinogenesis by directly or indirectly influencing tumour occurrence and development. Porphyromonas gingivalis is an important pathogen causing periodontitis, and periodontitis can promote the occurrence of various tumours. An increasing number of studies to date have shown that P. gingivalis plays an important role in the occurrence and development of oesophageal cancer. Overall, exploring how P. gingivalis promotes oesophageal cancer occurrence and development and how it affects the prognosis of these patients is of great importance for the diagnosis, prevention, and treatment of this type of cancer. Herein, the latest progress is reviewed.

We consider a spatial model of cancer in which cells are points on the d-dimensional torus $\mathcal{T}=[0,L]^d$, and each cell with $k-1$ mutations acquires a kth mutation at rate $\mu_k$. We assume that the mutation rates $\mu_k$ are increasing, and we find the asymptotic waiting time for the first cell to acquire k mutations as the torus volume tends to infinity. This paper generalizes results on waiting for $k\geq 3$ mutations in Foo et al. (2020), which considered the case in which all of the mutation rates $\mu_k$ are the same. In addition, we find the limiting distribution of the spatial distances between mutations for certain values of the mutation rates.