For Markov chains and Markov processes exhibiting a form of stochastic monotonicity (higher states have higher transition probabilities in terms of stochastic dominance), stability and ergodicity results can be obtained with the use of order-theoretic mixing conditions. We complement these results by providing quantitative bounds on deviations between distributions. We also show that well-known total variation bounds can be recovered as a special case.

Social networks influence health outcomes, yet declining health can also reshape social ties. While prior research has focused on constrained settings, the impact of health on social networks in fully voluntary contexts remains underexplored. This study examines the reciprocal relationship between health and social networks in voluntary settings, assessing whether previously observed patterns persist. We analyzed three-wave longitudinal whole network data from two voluntary clubs (N = 102, mean age = 54 years) in North-Rhine Westphalia, Germany, using Stochastic Actor-Oriented Models to distinguish between selection and influence effects across self-rated, mental, and physical health measures. Our analyses suggest diverging patterns observed in more constrained settings. We found no evidence of peer influence on health across any measures. While self-rated health showed some evidence of selection effects, social avoidance was limited to individuals with poor physical health. Notably, we found no evidence of withdrawal; instead, individuals with poorer health were more likely to nominate others in the network, suggesting they actively sought social connections as a compensatory strategy. These findings challenge existing assumptions about health-based network dynamics, emphasizing the need to reconsider how social networks function in voluntary contexts. Future research should explore how the degree of setting constraints shape health-related network dynamics.

In this paper, we solve an exit probability game between two players, each of whom controls a linear diffusion process. One player controls its process to minimize the probability that the difference of the processes reaches a low level before it reaches a high level, while the other player aims to maximize the probability. By solving the Bellman–Isaacs equations, we find the sub-value and sup-value functions of the game in explicit forms, which are twice continuously differentiable. The optimal plays associated with the sub-value and sup-value are also found explicitly.

West Nile virus (WNV) is a zoonotic mosquito-borne Flavivirus, with bird populations reservoirs. Although often asymptomatic, infection in humans can cause febrile symptoms and, more rarely, severe neurological symptoms. Previous studies assessed environmental drivers of WNV infections, but most overlooked areas with potential WNV circulation despite no reported human case, and mixed mechanisms affecting hosts vs. vectors. Our objective was to generate a WNV Bird Risk Index (BRI) mapping the potential of WNV circulation in bird communities across Europe. We first used a bird traits-based model to estimate WNV seroprevalence in European wild bird species and identify eco-ethological characteristics associated with it. This allowed us to build a map of the WNV BRI that showed a strong spatial heterogeneity across Europe. To validate this metric, using a Besag-York-Mollie 2 spatial model in a Bayesian framework, we showed a positive association between the BRI and the number of years with notified WNV human cases between 2016 and 2023, at the NUTS administrative region scale. To conclude, we provide a map quantifying the suitability for WNV to circulate in the bird reservoir. This allows to target surveillance efforts in areas at risk for WNV zoonotic infections in the future.

We prove new results about comparing the efficiency of general state space Markov chain Monte Carlo algorithms that randomly select a possibly different reversible method at each step (previously known only for finite state spaces). We also provide new, simpler, more accessible proofs of key results, and analyse numerous examples. We provide a full proof of the formula for the asymptotic variance for real-valued functionals on $\varphi$-irreducible reversible Markov chains, first introduced by Kipnis and Varadhan (1986, Commun. Math. Phys. 104, 1–19). Given two Markov kernels P and Q with stationary measure $\pi$, we say that the Markov kernel P efficiency-dominates the Markov kernel Q if the asymptotic variance with respect to P is at most the asymptotic variance with respect to Q for every real-valued functional $f\in L^2(\pi)$. Assuming only a basic background in functional analysis, we prove that for two reversible Markov kernels P and Q, P efficiency-dominates Q if and only if the operator $\mathcal{Q}-\mathcal{P}$, where $\mathcal{P}$ is the operator on $L^2(\pi)$ that maps $f\mapsto\int f(y)P(\cdot,\mathrm{d}y)$ and similarly for $\mathcal{Q}$, is positive on $L^2(\pi)$, i.e. $\langle f,\left(\mathcal{Q}-\mathcal{P}\right)f\rangle\geq0$ for every $f\in L^2(\pi)$ (previous proofs for general state spaces use technical results from monotone operator function theory). We use this result to show that under mild conditions, sandwich variants of data augmentation algorithms efficiency-dominate the original algorithm. We also provide other easy-to-check sufficient conditions for efficiency dominance, some of which are generalized from the finite state space case. We also provide a proof based on that of Tierney (1998, Ann. Appl. Prob. 8, 1–9) that Peskun dominance is a sufficient condition for efficiency dominance for reversible kernels. Using these results, we show that Markov kernels formed by random selection of other ‘component’ Markov kernels will always efficiency-dominate another Markov kernel formed in this way, as long as the component kernels of the former efficiency-dominate those of the latter. These results on the efficiency dominance of combining component kernels generalizes the results on the efficiency dominance of combined chains introduced by Neal and Rosenthal (2024, J. Appl. Prob. 62, 188–208) from finite state spaces to general state spaces.

This article studies the principal component analysis (PCA) estimation of weak factor models with sparse loadings. We uncover an intrinsic near-sparsity preservation property for the PCA estimators of loadings, which comes from the approximately (block) upper triangular structure of the rotation matrix. It suggests an asymmetric relationship among factors: the sparsity of the rotated loadings for a stronger factor can be contaminated by the loadings from weaker ones, but the sparsity of the rotated loadings of a weaker factor is almost unaffected by the loadings of stronger ones. Then, we propose a simple alternative to the existing penalized approaches to sparsify the loading estimators by screening out the small PCA loading estimators directly, and construct consistent estimators for factor strengths. The proposed estimators perform well in finite samples, as shown by a set of Monte Carlo simulations.

System components usually attain marginal lifetimes with stochastic dependence in the context of load-sharing reliability structures. This study deals with the load-sharing parallel systems of two components. We prove that two marginal lifetimes are positively quadrant dependent when component lifetimes have continuous probability distributions, and such a stochastic dependence is upgraded to the total positive of order 2 in the setting of component lifetimes having an exponential distribution. In addition, we discuss how these findings shed light on related results for the load-sharing Ross model, the conditional residual lifetime, and the conditional inactivity time.

In this paper, we study the joint distribution of the forward and backward recurrence times in a delayed renewal process, as well as their marginal distributions. We obtain several exact results and bounds for these quantities. Some of these bounds are “general,” in the sense that the bounds are valid for any arbitrary distributions of the inter-arrival times, and some are based on aging properties of the distributions of the interarrival times of the renewals. Finally, several numerical examples are presented to illustrate the results.

In a recent paper, Juodis and Reese (2022, Journal of Business & Economic Statistics, 40, 1191–1203) (JR) show that the application of the CD test proposed by Pesaran (2004, General diagnostic tests for cross-sectional dependence in panels, CWPE 0435, Cambridge) to residuals from panels with latent factors results in over-rejection. They propose a randomized test statistic to correct for over-rejection, and add a screening component to achieve power. This article considers the same problem but from a different perspective and shows that the standard CD test remains valid if the latent factors are weak. A bias-corrected version, CD$^{\ast}$, is proposed which is shown to be asymptotically standard normal under the null of error cross-sectional independence which has power against network-type alternatives. This result is shown to hold for pure latent factor models as well as for panel regression models with latent factors. The case where the errors are serially correlated is also considered. Small sample properties of the CD$^{\ast}$ test are investigated by Monte Carlo experiments and are shown to have satisfactory small sample properties. In an empirical application, using the CD$^{\ast}$ test, it is shown that there remains spatial error dependence in a panel data model for real house price changes across 377 Metropolitan Statistical Areas in the United States, even after the effects of latent factors are filtered out.

We analysed weekly influenza A intensive care unit (ICU) or high dependency unit (HDU) admissions reported by age group and subtype by NHS trusts in England through mandatory surveillance during the 2023–2024 influenza season. We investigated whether subtype reporting varied with patient age group, NHS trust type and region. We estimated the subtype ratio and explored whether this estimate varied among subsets of trusts grouped by the regularity of subtype reporting. Our aim was to explore factors relating to subtype reporting and investigate how these affect subtype ratio estimates. 112 NHS trusts reported data, with 86 trusts reporting influenza A cases and 28 trusts reporting subtyped influenza A cases. The proportion of subtype reporting trusts varied with region and trust type, but not patient age group. The estimated ratio of influenza A(H1N1)pdm09 to influenza A(H3N2) was 3.13 (95% CI: 2.17, 4.51), indicating that influenza A(H1N1)pdm09 was dominant; this was approximately similar across levels of regularity of trust subtype reporting. The accuracy of subtype ratio estimates depends on the availability of influenza A subtype information and data representativeness. We identified low levels of subtype reporting, which likely limits early recognition of new influenza strains and informing of the prescription of antivirals in influenza outbreaks.

Following the pivotal work of Sevastyanov (1957), who considered branching processes with homogeneous Poisson immigration, much has been done to understand the behaviour of such processes under different types of branching and immigration mechanisms. Recently, the case where the times of immigration are generated by a non-homogeneous Poisson process has been considered in depth. In this work, we demonstrate how we can use the framework of point processes in order to go beyond the Poisson process. As an illustration, we show how to transfer techniques from the case of Poisson immigration to the case where it is spanned by a determinantal point process.

We employ an appropriate change of measure technique to offer a general result connecting a general form of the Gerber–Shiu function with the distribution of the deficit at ruin under the new (exponentially tilted) measure. Exploiting this result, we extract closed-form formulae for special forms of the Gerber–Shiu function assuming two cases of bivariate distributions that describe the dependence structure between claim sizes and inter-claim times. More specifically, initially, we employ the Downton–Moran bivariate exponential distribution, and we offer explicit formulae for cases of the Gerber–Shiu functions that include the time and the number of claims until ruin. In addition, we derive a closed formula for the defective discounted joint density of the number of claims until ruin, the deficit at ruin, and the time until ruin. The same is achieved for the joint density of the number of claims and the deficit at ruin. We further generalize these results by assuming that the inter-claim times and the claim sizes follow a Kibble–Moran bivariate Erlang distribution. Finally, we offer numerical examples in order to illustrate our main results.

We evaluate the effect of reciprocal trust within pairs of individuals—gauged by total potential earnings in a trust experiment—on the probability of relationship formation, in comparison with well-known determinants of social ties, such as time of exposure and homophily along demographic traits. We measured trust and trustworthiness for every individual in an incoming cohort of undergraduate students before they began interacting. Using relationship data sourced from surveys and campus entry/exit times between one month and two years after the trust experiment, we find that reciprocal trust is neither a statistically nor an economically significant factor in determining the students’ social networks. Instead, time of exposure, prior acquaintance, and other demographic characteristics play important and persistent roles in relationship formation.

We revisit the question of how to include parameter uncertainty in univariate parametric models of losses and loss ratios. We first review the statistical theory for including parameter uncertainty based on right Haar priors (RHPs), which applies to many commonly used models. In this theory, the prior is chosen in such a way as to ensure matching between predicted probabilities and the relative frequencies of future outcomes in repeated tests. This property is known as reliability, or calibration. We then test priors for including parameter uncertainty in a number of models not covered by RHP theory. For these models, we find priors that generate predictions that are more reliable than predictions based on maximum likelihood, although they are not perfectly reliable. We discuss numerical schemes that can be used to generate Bayesian predictions, including a novel use of asymptotic expansions, and we include an example in which we show the impact of including parameter uncertainty in the modeling of extreme hurricane losses. The tail loss estimates show material increases due to the inclusion of parameter uncertainty. Finally, we describe a new software library that makes it straightforward to apply the methods we describe.

Shiga toxin-producing Escherichia coli (STEC) are zoonotic, foodborne pathogens that cause outbreaks of infectious gastrointestinal disease, including haemolytic uraemic syndrome (HUS) which can be fatal. In November 2023, a foodborne outbreak of STEC serotype O26:H11 stx2a/eae, involving 40 cases (54% female and 76% aged 0–9 years old), including 19 children with HUS. Whole-genome sequencing analysis revealed the outbreak strain was multidrug resistant and likely originated from outside the United Kingdom. Epidemiological analysis showed greatest odds of exposure among cases for consumption of a dried fruit product, predominantly in multi-packs. Batch numbers of the packs consumed by cases were rarely available, and where recorded, other packs in the same the batch were unavailable for testing; therefore, targeted microbiological testing was not possible. Fruit for drying can become contaminated when the crop is exposed to irrigation water or rainwater run off containing animal faeces. For STEC, where detection of the causative agent in food is challenging, we recommend establishing multi-source weight of evidence frameworks that promote the application of epidemiological and food chain evidence for public health action and the expansion of global surveillance networks to enhance the detection of foodborne threats at home and abroad.

In France, HIV prevention measures including HIV testing, treatment, and uptake of pre-exposure prophylaxis (PrEP), have increased throughout the last decade. To analyse their impact, we performed a time series analysis of monthly HIV diagnoses reported via the national HIV surveillance database. In addition, we compared the timing of HIV promotional campaigns with monthly trends in HIV testing and PrEP initiation. From January 2012 to December 2022, new HIV diagnoses steadily decreased among men who have sex with men (MSM) born in France and heterosexuals born in France, whereas HIV diagnoses increased among MSM born abroad. HIV testing activity and PrEP use in France both steadily increased from 2014 to 2020, during which multiple campaigns targeting HIV testing and prevention occurred. The decline in HIV diagnoses among MSM born in France preceded the introduction of PrEP in 2016 and continued post-2016 without any acceleration in the rate of decline. Increased awareness of, access to and uptake of HIV prevention measures remain essential to progress towards HIV elimination in France, especially among MSM born abroad.

Panel data often contain stayers and slow movers. The literature proposes an estimator for the average partial effects (APEs) for this setting without a formal theory. The literature is also silent about inference in the presence of stayers and many slow movers. We contribute to this state of the art. First, we develop an asymptotic theory to guarantee that such an estimator is consistent in the presence of stayers and slow movers. Second, we propose its standard error. Third, we relax the existing assumption to allow for “many” slow movers. Fourth, we generalize the existing estimator. Fifth, we establish that this generalized estimator can achieve larger extents of bias reduction and hence faster convergence rates. Simulation studies demonstrate that the conventional 95% confidence interval covers the true value of the APE with 37%–93% frequencies whereas our proposed one achieves 93%–96% coverage frequencies. Using the U.S. Panel Study of Income Dynamics, we find that estimates of the marginal propensity to consume based on our generalized estimator remarkably differ in values from those of the existing estimators. Moreover, the generalized estimator achieves more than three times as small standard errors as those of the existing robust estimator.

Community-acquired pneumonia (CAP) remains an important public-health problem, and the COVID-19 pandemic and non-pharmaceutical interventions (NPIs) may have altered its burden. This study aimed to provide updated CAP burden among adults in Shanghai from 2016–2023.We analysed 61,230 participants aged 20–74 years from the Shanghai Suburban Adult Cohort and Biobank. CAP episodes were ascertained via ICD codes and clinical diagnoses. We calculated incidence rates before, during, and after NPIs, conducted subgroup analyses by age, sex, comorbidity and lifestyle. We used Poisson regression to compare stages, and Cox models to identify risk factors. The Overall CAP incidence was 42.1 per 1,000 person–years (95% CI 41.3–42.8). Incidence declined during NPIs (24.2/1,000 py) and rose after NPIs (95.9/1,000 py). The inpatient-to-outpatient ratio increased to 10.1% during NPIs and fell to 5.7% post–NPI. Among those without underlying conditions, rates were 40.1, 20.1 and 73.6/1,000 py before, during and after NPIs. Incidence was higher in participants ≥60 years and in those with multiple comorbidities, especially respiratory diseases. CAP burden temporarily fell during NPIs but resurged post–NPI, notably among high–risk groups. These findings highlight the need for targeted preventive strategies and continued CAP surveillance in the post-pandemic era.