We consider a stochastic model, called the replicator coalescent, describing a system of blocks of k different types that undergo pairwise mergers at rates depending on the block types: with rate $C_{ij}\geq 0$ blocks of type i and j merge, resulting in a single block of type i. The replicator coalescent can be seen as a generalisation of Kingman’s coalescent death chain in a multi-type setting, although without an underpinning exchangeable partition structure. The name is derived from a remarkable connection between the instantaneous dynamics of this multi-type coalescent when issued from an arbitrarily large number of blocks, and the so-called replicator equations from evolutionary game theory. By dilating time arbitrarily close to zero, we see that initially, on coming down from infinity, the replicator coalescent behaves like the solution to a certain replicator equation. Thereafter, stochastic effects are felt and the process evolves more in the spirit of a multi-type death chain.

The primary focus of this article is to capture heterogeneous treatment effects measured by the conditional average treatment effect. A model averaging estimation scheme is proposed with multiple candidate linear regression models under heteroskedastic errors, and the properties of this scheme are explored analytically. First, it is shown that our proposal is asymptotically optimal in the sense of achieving the lowest possible squared error. Second, the convergence of the weights determined by our proposal is provided when at least one of the candidate models is correctly specified. Simulation results in comparison with several related existing methods favor our proposed method. The method is applied to a dataset from a labor skills training program.

In March 2024, the East Midlands Health Protection Team was notified of a case of invasive Group A Streptococcus (iGAS) infection in an elderly care home resident. Twenty-two days later, another case in a resident from the same floor of the care home was notified. In accordance with national guidelines, an outbreak was declared, and a multidisciplinary outbreak control team (OCT) was urgently convened. Screening for GAS throat carriage was undertaken for staff and residents, excluding those receiving end-of-life care. All isolates were strain typed and characterised. Infection prevention and control (IPC) visits were undertaken to provide ongoing support. Screening identified five residents and five staff members positive for GAS. Antibiotic prophylaxis was provided to all staff throughout the setting (n = 74) and all residents on the affected floor (n = 35). Three individuals were positive on repeat screening. All staff and residents screened negative after 4 months and the two clinical cases recovered. Eleven of the 12 GAS isolates were identified as emm 3.93. This outbreak highlighted the importance of rapid screening, possible only through the deployment of a dedicated team, and rescreening post-decolonising treatment, as a means to contain such outbreaks.

Lower COVID-19 vaccination coverage was observed among some populations with a migration background in the Netherlands. This study examined determinants of being unvaccinated against COVID-19 in the primary vaccination round in adults and in the 2022 autumn booster round in persons aged ≥60 years, among four populations of non-Dutch origin with below average vaccination coverage: Moroccan, Turkish, Surinamese and Dutch-Caribbean, and persons of Dutch origin. We performed a population-wide register-based study, examining associations between potential determinants and being unvaccinated using multivariable logistic regression and computing population attributable fractions. Being a migrant with two foreign-born parents, younger age, living in highly/extremely urban areas and having a lower income, lower education level and low medical risk for severe COVID-19 were risk factors for being unvaccinated in all populations. Substantial differences in the (strength of) determinants and population attributable fractions between populations were also observed. Socioeconomic status only partially mediated the association with being a migrant with two foreign-born parents. These findings illustrate that interventions targeting specific ethnic minority and migrant populations need further study with the aim to optimize the impact of vaccination programmes and improve health equity. To understand reasons behind non-uptake and design (community-based) interventions, qualitative and survey-based research is needed.

This paper has been prepared by the IFoA’s Collective Defined Contribution (CDC) working party. The purpose is to raise awareness within the actuarial community and pensions industry on the wide range of design options and considerations for CDC solutions, together with a set of principles for the design work, which we believe should apply in most cases. This should also aid understanding of why different designs are better in different circumstances, and why some designs might have certain features that others would avoid.

Determining the factors that impact the risk for infection with SARS-CoV-2 is a priority as the virus continues to infect people worldwide. The objective was to determine the effectiveness of vaccines and other factors associated with infection among Canadian healthcare workers (HCWs) followed from 15 June 2020 to 1 December 2023. We also investigate the association between antibodies to SARS-CoV-2 and subsequent infections with SARS-CoV-2. Of the 2474 eligible participants, 2133 (86%) were female, 33% were nurses, the median age was 41 years, and 99.3% had received at least two doses of COVID-19 vaccine by 31 December 2021. The incidence of SARS-CoV-2 was 0.91 per 1000 person-days. Prior to the circulation of the Omicron variants, vaccine effectiveness (VE) was estimated at 85% (95% CI 1, 98) for participants who received the primary series of vaccine. During the Omicron period, relative adjusted VE was 43% (95% CI 29, 54), 56% (95% CI 42, 67), and 46% (95% CI 24, 62) for 3, 4, and ≥ 5 doses compared with those who received primary series after adjusting for previous infection and other covariates. Exposure to infected household members, coworkers, or friends in the previous 14 days were risk factor for infection, while contact with an infected patient was not statistically significant. Participants with higher levels of immunoglobulin G (IgG) anti-receptor binding domain (RBD) antibodies had lower rates of infection than those with the lowest levels. COVID-19 vaccines remained effective throughout the follow-up of this cohort of highly vaccinated HCWs. IgG anti-RBD antibody levels may be useful as correlates of protection for issues such as vaccine development and testing. There remains a need to increase the awareness among HCWs about the risk of contracting SARS-CoV-2 from contacts at a variety of venues.

Actuaries must model mortality to understand, manage and price risk. Continuous-time methods offer considerable practical benefits to actuaries analysing portfolio mortality experience. This paper discusses six categories of advantage: (i) reflecting the reality of data produced by everyday business practices, (ii) modelling rapid changes in risk, (iii) modelling time- and duration-varying risk, (iv) competing risks, (v) data-quality checking and (vi) management information. Specific examples are given where continuous-time models are more useful in practice than discrete-time models.

Competing and complementary risk (CCR) problems are often modelled using a class of distributions of the maximum, or minimum, of a random number of independent and identically distributed random variables, called the CCR class of distributions. While CCR distributions generally do not have an easy-to-calculate density or probability mass function, two special cases, namely the Poisson–exponential and exponential–geometric distributions, can easily be calculated. Hence, it is of interest to approximate CCR distributions with these simpler distributions. In this paper, we develop Stein’s method for the CCR class of distributions to provide a general comparison method for bounding the distance between two CCR distributions, and we contrast this approach with bounds obtained using a Lindeberg argument. We detail the comparisons for Poisson–exponential, and exponential–geometric distributions.

We reprise some common statistical models for actuarial mortality analysis using grouped counts. We then discuss the benefits of building mortality models from the most elementary items. This has two facets. First, models are better based on the mortality of individuals, rather than groups. Second, models are better defined in continuous time, rather than over fixed intervals like a year. We show how Poisson-like likelihoods at the “macro” level are built up by product integration of sequences of infinitesimal Bernoulli trials at the “micro” level. Observed data is represented through a stochastic mortality hazard rate, and counting processes provide the natural notation for left-truncated and right-censored actuarial data, individual or age-grouped. Together these explain the “pseudo-Poisson” behaviour of survival model likelihoods.

Stochastic actor-oriented models (SAOMs) were designed in the social network setting to capture network dynamics representing a variety of influences on network change. The standard framework assumes the observed networks are free of false positive and false negative edges, which may be an unrealistic assumption. We propose a hidden Markov model (HMM) extension to these models, consisting of two components: 1) a latent model, which assumes that the unobserved, true networks evolve according to a Markov process as they do in the SAOM framework; and 2) a measurement model, which describes the conditional distribution of the observed networks given the true networks. An expectation-maximization algorithm is developed for parameter estimation. We address the computational challenge posed by a massive discrete state space, of a size exponentially increasing in the number of vertices, through the use of the missing information principle and particle filtering. We present results from a simulation study, demonstrating our approach offers improvement in accuracy of estimation, in contrast to the standard SAOM, when the underlying networks are observed with noise. We apply our method to functional brain networks inferred from electroencephalogram data, revealing larger effect sizes when compared to the naive approach of fitting the standard SAOM.

This systematic review synthesized evidence on the viral load of severe acute respiratory syndrome coronavirus-2 (SARS-CoV-2) shedding in exhaled material to understand how the exhaled SARS-CoV-2 viral load of infected individuals varies with days since exposure. Medline, Scopus, and Web of Science databases were searched using a combination of search terms to identify articles that tested exhaled material from SARS-CoV-2 infected patients. Records were systematically screened and assessed for eligibility, following which reference lists of eligible articles were hand-searched to identify further relevant studies. Data extraction and quality assessment of individual studies were conducted prior to synthesizing the evidence. Forty-five articles that sampled exhaled breath, exhaled breath condensate, face masks, and cough samples were reviewed. The variation in the SARS-CoV-2 viral load in these materials was considerable with the detection of viral RNA shed during breathing as far as 43 days after symptom onset. The replication-competent virus was present in all four sample types, with the majority isolated during the first week of symptoms onset. Variations in the sample types and testing protocols precluded meta-analysis. High heterogeneity in exhaled SARS-CoV-2 viral load is likely due to host and viral factors as well as variations in sampling and diagnostic methodologies. Evidence on SARS-CoV-2 shedding in exhaled material is scarce and more controlled fundamental studies are needed to assess this important route of viral shedding.

The classical credibility premium provides a simple and efficient method for predicting future damages and losses. However, when dealing with a nonhomogeneous population, this widely used technique has been challenged by the Regression Tree Credibility (RTC) model and the Logistic Regression Credibility (LRC) model. This article introduces the Mixture Credibility Formula (MCF), which represents a convex combination of the classical credibility premiums of several homogeneous subpopulations derived from the original population. We also compare the performance of the MCF method with the RTC and LRC methods. Our analysis demonstrates that the MCF method consistently outperforms these approaches in terms of the quadratic loss function, highlighting its effectiveness in refining insurance premium calculations and enhancing risk assessment strategies.

We consider stationary configurations of points in Euclidean space that are marked by positive random variables called scores. The scores are allowed to depend on the relative positions of other points and outside sources of randomness. Such models have been thoroughly studied in stochastic geometry, e.g. in the context of random tessellations or random geometric graphs. It turns out that in a neighborhood of a point with an extreme score it is possible to rescale positions and scores of nearby points to obtain a limiting point process, which we call the tail configuration. Under some assumptions on dependence between scores, this local limit determines the global asymptotics for extreme scores within increasing windows in $\mathbb{R}^d$. The main result establishes the convergence of rescaled positions and clusters of high scores to a Poisson cluster process, quantifying the idea of the Poisson clumping heuristic by Aldous (1989, in the point process setting). In contrast to the existing results, our framework allows for explicit calculation of essentially all extremal quantities related to the limiting behavior of extremes. We apply our results to models based on (marked) Poisson processes where the scores depend on the distance to the kth nearest neighbor and where scores are allowed to propagate through a random network of points depending on their locations.

Simulations of critical phenomena, such as wildfires, epidemics, and ocean dynamics, are indispensable tools for decision-making. Many of these simulations are based on models expressed as Partial Differential Equations (PDEs). PDEs are invaluable inductive inference engines, as their solutions generalize beyond the particular problems they describe. Methods and insights acquired by solving the Navier–Stokes equations for turbulence can be very useful in tackling the Black-Scholes equations in finance. Advances in numerical methods, algorithms, software, and hardware over the last 60 years have enabled simulation frontiers that were unimaginable a couple of decades ago. However, there are increasing concerns that such advances are not sustainable. The energy demands of computers are soaring, while the availability of vast amounts of data and Machine Learning(ML) techniques are challenging classical methods of inference and even the need of PDE based forecasting of complex systems. I believe that the relationship between ML and PDEs needs to be reset. PDEs are not the only answer to modeling and ML is not necessarily a replacement, but a potent companion of human thinking. Algorithmic alloys of scientific computing and ML present a disruptive potential for the reliable and robust forecasting of complex systems. In order to achieve these advances, we argue for a rigorous assessment of their relative merits and drawbacks and the adoption of probabilistic thinking for developing complementary concepts between ML and scientific computing. The convergence of AI and scientific computing opens new horizons for scientific discovery and effective decision-making.

We study convergence rates, in mean, for the Hausdorff metric between a finite set of stationary random variables and their common support, which is supposed to be a compact subset of $\mathbb{R}^d$. We propose two different approaches for this study. The first is based on the notion of a minimal index. This notion is introduced in this paper. It is in the spirit of the extremal index, which is much used in extreme value theory. The second approach is based on a $\beta$-mixing condition together with a local-type dependence assumption. More precisely, all our results concern stationary $\beta$-mixing sequences satisfying a tail condition, known as the (a, b)-standard assumption, together with a local-type dependence condition or stationary sequences satisfying the (a, b)-standard assumption and having a positive minimal index. We prove that the optimal rates of the independent and identically distributed setting can be reached. We apply our results to stationary Markov chains on a ball, or to a class of Markov chains on a circle or on a torus. We study with simulations the particular examples of a Möbius Markov chain on the unit circle and of a Markov chain on the unit square wrapped on a torus.

Previously, we reported the persistence of the bacterial pathogen Neisseria meningitidis on fomites, indicating a potential route for environmental transmission. The current goal was to identify proteins that vary among strains of meningococci that have differing environmental survival. We carried out a proteomic analysis of two strains that differ in their potential for survival outside the host. The Group B epidemic strain NZ98/254 and Group W carriage strain H34 were cultured either at 36 °C, 5% CO2, and 95% relative humidity (RH) corresponding to host conditions in the nasopharynx, or at lower humidities of 22% or 30% RH at 30 °C, for which there was greater survival on fomites. For NZ98/254, the shift to lower RH and temperature was associated with increased abundance of proteins involved in metabolism, stress responses, and outer membrane components, including pili and porins. In contrast, H34 responded to lower RH by decreasing the abundance of multiple proteins, indicating that the lower viability of H34 may be linked to decreased capacity to mount core protective responses. The results provide a snapshot of bacterial proteins and metabolism that may be related to normal fitness, to the greater environmental persistence of NZ98/254 compared to H34, and potentially to differences in transmission and pathogenicity.

This work concerns stochastic differential equations with jumps. We prove convergence for solutions to a sequence of (possibly degenerate) stochastic differential equations with jumps when the coefficients converge in some appropriate sense. Then some special cases are analyzed and some concrete and verifiable conditions are given.