In the traditional multidimensional credibility models developed by Jewell ((1973) Operations Research Center, pp. 73–77.), the estimation of the hypothetical mean vector involves complex matrix manipulations, which can be challenging to implement in practice. Additionally, the estimation of hyperparameters becomes even more difficult in high-dimensional risk variable scenarios. To address these issues, this paper proposes a new multidimensional credibility model based on the conditional joint distribution function for predicting future premiums. First, we develop an estimator of the joint distribution function of a vector of claims using linear combinations of indicator functions based on past observations. By minimizing the integral of the expected quadratic distance function between the proposed estimator and the true joint distribution function, we obtain the optimal linear Bayesian estimator of the joint distribution function. Using the plug-in method, we obtain an explicit formula for the multidimensional credibility estimator of the hypothetical mean vector. In contrast to the traditional multidimensional credibility approach, our newly proposed estimator does not involve a matrix as the credibility factor, but rather a scalar. This scalar is composed of both population information and sample information, and it still maintains the essential property of increasingness with respect to the sample size. Furthermore, the new estimator based on the joint distribution function can be naturally extended and applied to estimate the process covariance matrix and risk premiums under various premium principles. We further illustrate the performance of the new estimator by comparing it with the traditional multidimensional credibility model using bivariate exponential-gamma and multivariate normal distributions. Finally, we present two real examples to demonstrate the findings of our study.

Collecting network data directly from network members can be challenging. One alternative involves inferring a network from observed groups, for example, inferring a network of scientific collaboration from researchers’ observed paper authorships. In this paper, I explore when an unobserved undirected network of interest can accurately be inferred from observed groups. The analysis uses simulations to experimentally manipulate the structure of the unobserved network to be inferred, the number of groups observed, the extent to which the observed groups correspond to cliques in the unobserved network, and the method used to draw inferences. I find that when a small number of groups are observed, an unobserved network can be accurately inferred using a simple unweighted two-mode projection, provided that each group’s membership closely corresponds to a clique in the unobserved network. In contrast, when a large number of groups are observed, an unobserved network can be accurately inferred using a statistical backbone extraction model, even if the groups’ memberships are mostly random. These findings offer guidance for researchers seeking to indirectly measure a network of interest using observations of groups.

We explore the limiting spectral distribution of large-dimensional random permutation matrices, assuming the underlying population distribution possesses a general dependence structure. Let $\textbf X = (\textbf x_1,\ldots,\textbf x_n)$ $\in \mathbb{C} ^{m \times n}$ be an $m \times n$ data matrix after self-normalization (n samples and m features), where $\textbf x_j = (x_{1j}^{*},\ldots, x_{mj}^{*} )^{*}$. Specifically, we generate a permutation matrix $\textbf X_\pi$ by permuting the entries of $\textbf x_j$ $(j=1,\ldots,n)$ and demonstrate that the empirical spectral distribution of $\textbf {B}_n = ({m}/{n})\textbf{U} _{n} \textbf{X} _\pi \textbf{X} _\pi^{*} \textbf{U} _{n}^{*}$ weakly converges to the generalized Marčenko–Pastur distribution with probability 1, where $\textbf{U} _n$ is a sequence of $p \times m$ non-random complex matrices. The conditions we require are $p/n \to c >0$ and $m/n \to \gamma > 0$.

The betweenness centrality of a graph vertex measures how often this vertex is visited on shortest paths between other vertices of the graph. In the analysis of many real-world graphs or networks, the betweenness centrality of a vertex is used as an indicator for its relative importance in the network. In particular, it is among the most popular tools in social network analysis. In recent years, a growing number of real-world networks have been modeled as temporal graphs instead of conventional (static) graphs. In a temporal graph, we have a fixed set of vertices and there is a finite discrete set of time steps, and every edge might be present only at some time steps. While shortest paths are straightforward to define in static graphs, temporal paths can be considered “optimal” with respect to many different criteria, including length, arrival time, and overall travel time (shortest, foremost, and fastest paths). This leads to different concepts of temporal betweenness centrality, posing new challenges on the algorithmic side. We provide a systematic study of temporal betweenness variants based on various concepts of optimal temporal paths.

Computing the betweenness centrality for vertices in a graph is closely related to counting the number of optimal paths between vertex pairs. While in static graphs computing the number of shortest paths is easily doable in polynomial time, we show that counting foremost and fastest paths is computationally intractable (#P-hard), and hence, the computation of the corresponding temporal betweenness values is intractable as well. For shortest paths and two selected special cases of foremost paths, we devise polynomial-time algorithms for temporal betweenness computation. Moreover, we also explore the distinction between strict (ascending time labels) and non-strict (non-descending time labels) time labels in temporal paths. In our experiments with established real-world temporal networks, we demonstrate the practical effectiveness of our algorithms, compare the various betweenness concepts, and derive recommendations on their practical use.

Rectal swabs of 104 patients who underwent abdominal surgery were screened for ESBL producers. Sequence types (STs) and resistance genes were identified by whole-genome sequencing of 46 isolates from 17 patients. All but seven isolates were assigned to recognized STs. While 18 ESBL-producing E. coli (EPEC) strains were of unique STs, ESBL-producing K. pneumoniae (EPKP) strains were mainly ST14 or ST15. Eight patients harboured strains of the same ST before and after abdominal surgery. The most prevalent resistant genes in E. coli were blaEC (69.57%), blaCTX-M (65.22%), and blaTEM (36.95%), while blaSHV was present in only K. pneumoniae (41.30%). Overall, genes encoding β-lactamases of classes A (blaCTX-M, blaTEM, blaZ), C (blaSHV, blaMIR, and blaDHA), and D (blaOXA) were identified, the most prevalent variants being blaCTX-M-15, blaTEM-1B, blaSHV-28, and blaOXA-1. Interestingly, blaCMY-2, the most common pAmpC β-lactamase genes reported worldwide, and mobile colistin resistance genes, mcr-10-1, were also identified. The presence of blaCMY-2 and mcr-10-1 is concerning as they may constitute a potentially high risk of pan-resistant post-surgical infections. It is imperative that healthcare professionals monitor intra-abdominal surgical site infections rigorously to prevent transmission of faecal ESBL carriage in high-risk patients.

Ross River virus (RRV), the most medically and economically important arbovirus in Australia, has been the most prevalent arbovirus infections in humans for many years. Infected humans and horses often suffer similar clinical symptoms. We conducted a prospective longitudinal study over a 3.5-year period to investigate the exposure dynamics of RRV in three foal cohorts (n = 32) born in a subtropical region of South East Queensland, Australia, between 2020 and 2022. RRV-specific seroconversion was detected in 56% (n = 18) of foals with a median time to seroconversion, after waning of maternal antibodies, of 429 days (95% CI: 294–582). The median age at seroconversion was 69 weeks (95% CI: 53–57). Seroconversion events were only detected between December and March (Southern Hemisphere summer) over the entire study period. Cox proportion hazards regression analyses revealed that seroconversions were significantly (p < 0.05) associated with air temperature in the month of seroconversion. Time-lags in meteorological variables were not significantly (p > 0.05) associated with seroconversion, except for relative humidity (p = 0.036 at 2-month time-lag). This is in contrast to research results of RRV infection in humans, which peaked between March and May (Autumn) and with a 0–3 month time-lag for various meteorological risk factors. Therefore, horses may be suitable sentinels for monitoring active arbovirus circulation and could be used for early arbovirus outbreak detection in human populations.

The global incidence of syphilis is increasing. Continuity of care challenges the control of sexually transmitted diseases. In this study, we assessed the follow-up and serological decline differences between community- and hospital-diagnosed patients in Israel. A historical cohort study was conducted using the Israel National Syphilis Center (NSC) repository. Patients with a positive non-specific Venereal Disease Research Laboratory (VDRL) test between 2011 and 2020 were included. Rates of serological follow-up and serological titre decreases were compared between hospital- and community-diagnosed patients. The study included 4,445 patients, 2,596 (58.4%) were diagnosed in community clinics and 1,849 (41.6%) in hospitals. Of community-diagnosed patients, 1,957 (75.4%) performed follow-up testing, compared with 834 (51.2%) hospital-diagnosed patients (p < 0.001). On multivariate analysis, the odds ratio of serology follow-up among community-diagnosed patients was 2.8 (95 per cent confidence interval (95% CI): 2.2–3.5) that of hospital-diagnosed patients. There were 1,397 (71.4%) community-diagnosed patients with serological titre decrease, compared with 626 (74.9%) hospital-diagnosed patients (p = 0.03). On multivariate analysis, this difference diminished. Serological follow-up testing is suboptimal and was performed more often among patients initially diagnosed in the community compared to hospitals. Continuity of care should be improved to promote successful patient care and prevent disease spread.

The protection number of a vertex $v$ in a tree is the length of the shortest path from $v$ to any leaf contained in the maximal subtree where $v$ is the root. In this paper, we determine the distribution of the maximum protection number of a vertex in simply generated trees, thereby refining a recent result of Devroye, Goh, and Zhao. Two different cases can be observed: if the given family of trees allows vertices of outdegree $1$, then the maximum protection number is on average logarithmic in the tree size, with a discrete double-exponential limiting distribution. If no such vertices are allowed, the maximum protection number is doubly logarithmic in the tree size and concentrated on at most two values. These results are obtained by studying the singular behaviour of the generating functions of trees with bounded protection number. While a general distributional result by Prodinger and Wagner can be used in the first case, we prove a variant of that result in the second case.

High-cardinality categorical features are pervasive in actuarial data (e.g., occupation in commercial property insurance). Standard categorical encoding methods like one-hot encoding are inadequate in these settings.

In this work, we present a novel Generalised Linear Mixed Model Neural Network (“GLMMNet”) approach to the modelling of high-cardinality categorical features. The GLMMNet integrates a generalised linear mixed model in a deep learning framework, offering the predictive power of neural networks and the transparency of random effects estimates, the latter of which cannot be obtained from the entity embedding models. Further, its flexibility to deal with any distribution in the exponential dispersion (ED) family makes it widely applicable to many actuarial contexts and beyond. In order to facilitate the application of GLMMNet to large datasets, we use variational inference to estimate its parameters—both traditional mean field and versions utilising textual information underlying the high-cardinality categorical features.

We illustrate and compare the GLMMNet against existing approaches in a range of simulation experiments as well as in a real-life insurance case study. A notable feature for both our simulation experiment and the real-life case study is a comparatively low signal-to-noise ratio, which is a feature common in actuarial applications. We find that the GLMMNet often outperforms or at least performs comparably with an entity-embedded neural network in these settings, while providing the additional benefit of transparency, which is particularly valuable in practical applications.

Importantly, while our model was motivated by actuarial applications, it can have wider applicability. The GLMMNet would suit any applications that involve high-cardinality categorical variables and where the response cannot be sufficiently modelled by a Gaussian distribution, especially where the inherent noisiness of the data is relatively high.

We explore some of the risks related to Artificial Intelligence (AI) from an actuarial perspective based on research from a transregional industry focus group. We aim to define the key gaps and challenges faced when implementing and utilising modern modelling techniques within traditional actuarial tasks from a risk perspective and in the context of professional standards and regulations. We explore best practice guidelines to attempt to define an ideal approach and propose potential next steps to help reach the ideal approach. We aim to focus on the considerations, initially from a traditional actuarial perspective and then, if relevant, consider some implications for non-traditional actuarial work, by way of examples. The examples are not intended to be exhaustive. The group considered potential issues and challenges of using AI, related to the following key themes:

• Ethical

  • ○ Bias, fairness, and discrimination

  • ○ Individualisation of risk assessment

  • ○ Public interest

• Professional

  • ○ Interpretability and explainability

  • ○ Transparency, reproducibility, and replicability

  • ○ Validation and governance

• Lack of relevant skills available

• Wider themes

This paper aims to provide observations that could help inform industry and professional guidelines or discussion or to support industry practitioners. It is not intended to replace current regulation, actuarial standards, or guidelines. The paper is aimed at an actuarial and insurance technical audience, specifically those who are utilising or developing AI, and actuarial industry bodies.

The Internet of Things (IoT) and wearable computing are crucial elements of modern information systems and applications in which advanced features for user interactivity and monitoring are required. However, in the fields of pervasive gaming, IoT has had limited real-world applications. In this work, we present a prototype of a wearable platform for pervasive games that combines IoT with wearable computing to enable the real-time monitoring of physical activity. The main objective of the solution is to promote the utilization of gamification techniques to enhance the physical activity of users through challenges and quests. This aims to create a symbolic link between the virtual gameplay and the real-world environment without the requirement of a smartphone. With the integration of sensors and wearable devices by design, the platform has the capability of real-time monitoring the users’ physical activity during the game. The system performance results highlight the efficiency and attractiveness of the wearable platform for gamifying physical activity.

Compressible anisothermal flows, which are commonly found in industrial settings such as combustion chambers and heat exchangers, are characterized by significant variations in density, viscosity, and heat conductivity with temperature. These variations lead to a strong interaction between the temperature and velocity fields that impacts the near-wall profiles of both quantities. Wall-modeled large-eddy simulations (LESs) rely on a wall model to provide a boundary condition, for example, the shear stress and the heat flux that accurately represents this interaction despite the use of coarse cells near the wall, and thereby achieve a good balance between computational cost and accuracy. In this article, the use of graph neural networks for wall modeling in LES is assessed for compressible anisothermal flow. Graph neural networks are a type of machine learning model that can learn from data and operate directly on complex unstructured meshes. Previous work has shown the effectiveness of graph neural network wall modeling for isothermal incompressible flows. This article develops the graph neural network architecture and training to extend their applicability to compressible anisothermal flows. The model is trained and tested a priori using a database of both incompressible isothermal and compressible anisothermal flows. The model is finally tested a posteriori for the wall-modeled LES of a channel flow and a turbine blade, both of which were not seen during training.

This paper examines the potential role of network analysis in understanding the powerful elites that pose a significant threat to peace and state-building within post-conflict contexts. This paper makes a threefold contribution. First, it identifies a caveat in the scholarship surrounding international interventions, shedding light on shortcomings in their design and implementation strategies, and elucidating the influence these elites wield in the political and economic realms. Next, it delineates the essentials of the network analysis approach, addressing the information and data requirements and limitations inherent in its application in conflict environments. Finally, the paper provides valuable insights gleaned from the international operation in Guatemala known as the International Commission for Impunity in Guatemala, which specifically targeted illicit networks. The argument asserts that network analysis functions as a dual-purpose tool—serving as both a descriptive instrument to reveal, identify, and address the root causes of conflict and a predictive tool to enhance peace agreement implementation and improve decision-making. Simultaneously, it underscores the challenge of data analysis and translating network interventions into tangible real-life consequences for long-lasting results.

We introduce a novel preferential attachment model using the draw variables of a modified Pólya urn with an expanding number of colors, notably capable of modeling influential opinions (in terms of vertices of high degree) as the graph evolves. Similar to the Barabási-Albert model, the generated graph grows in size by one vertex at each time instance; in contrast however, each vertex of the graph is uniquely characterized by a color, which is represented by a ball color in the Pólya urn. More specifically at each time step, we draw a ball from the urn and return it to the urn along with a number of reinforcing balls of the same color; we also add another ball of a new color to the urn. We then construct an edge between the new vertex (corresponding to the new color) and the existing vertex whose color ball is drawn. Using color-coded vertices in conjunction with the time-varying reinforcing parameter allows for vertices added (born) later in the process to potentially attain a high degree in a way that is not captured in the Barabási-Albert model. We study the degree count of the vertices by analyzing the draw vectors of the underlying stochastic process. In particular, we establish the probability distribution of the random variable counting the number of draws of a given color which determines the degree of the vertex corresponding to that color in the graph. We further provide simulation results presenting a comparison between our model and the Barabási-Albert network.

A version of the classical Buffon problem in the plane naturally extends to the setting of any Riemannian surface with constant Gaussian curvature. The Buffon probability determines a Buffon deficit. The relationship between Gaussian curvature and the Buffon deficit is similar to the relationship that the Bertrand–Diguet–Puiseux theorem establishes between Gaussian curvature and both circumference and area deficits.

Previous studies suggest that influenza virus infection may provide temporary non-specific immunity and hence lower the risk of non-influenza respiratory virus infection. In a randomized controlled trial of influenza vaccination, 1 330 children were followed-up in 2009–2011. Respiratory swabs were collected when they reported acute respiratory illness and tested against influenza and other respiratory viruses. We used Poisson regression to compare the incidence of non-influenza respiratory virus infection before and after influenza virus infection. Based on 52 children with influenza B virus infection, the incidence rate ratio (IRR) of non-influenza respiratory virus infection after influenza virus infection was 0.47 (95% confidence interval: 0.27–0.82) compared with before infection. Simulation suggested that this IRR was 0.87 if the temporary protection did not exist. We identified a decreased risk of non-influenza respiratory virus infection after influenza B virus infection in children. Further investigation is needed to determine if this decreased risk could be attributed to temporary non-specific immunity acquired from influenza virus infection.

We give algorithms for approximating the partition function of the ferromagnetic $q$-color Potts model on graphs of maximum degree $d$. Our primary contribution is a fully polynomial-time approximation scheme for $d$-regular graphs with an expansion condition at low temperatures (that is, bounded away from the order-disorder threshold). The expansion condition is much weaker than in previous works; for example, the expansion exhibited by the hypercube suffices. The main improvements come from a significantly sharper analysis of standard polymer models; we use extremal graph theory and applications of Karger’s algorithm to count cuts that may be of independent interest. It is #BIS-hard to approximate the partition function at low temperatures on bounded-degree graphs, so our algorithm can be seen as evidence that hard instances of #BIS are rare. We also obtain efficient algorithms in the Gibbs uniqueness region for bounded-degree graphs. While our high-temperature proof follows more standard polymer model analysis, our result holds in the largest-known range of parameters $d$ and $q$.

We consider the super-replication problem for a class of exotic options known as life-contingent options within the framework of the Black–Scholes market model. The option is allowed to be exercised if the death of the option holder occurs before the expiry date, otherwise there is a compensation payoff at the expiry date. We show that there exists a minimal super-replication portfolio and determine the associated initial investment. We then give a characterisation of when replication of the option is possible. Finally, we give an example of an explicit super-replicating hedge for a simple life-contingent option.