This article develops a new test to detect changes in generalized autoregressive conditionally heteroscedastic (GARCH(1,1)) processes without imposing a stationary assumption. Specifically, the procedure tests the null hypothesis of a GARCH process with constant parameters, either in (strictly) stationary or explosive regimes, against the alternative hypothesis of parameter changes. We derive the limiting distribution of the test statistics and establish their asymptotic consistency. Monte Carlo simulations show that the proposed test has good size control and high power. We demonstrate a prototype application on a small group of stocks and report a further extensive application to more than ten thousand U.S. stocks.

Measuring waning in vaccine effectiveness (VE) is challenging due to potential depletion-of-susceptibles bias. Some SARS-CoV-2 studies excluded individuals with prior infection and adjusted for the probability of remaining uninfected. We applied this approach to assess waning influenza VE in Hong Kong during the 2012/2013 season. First, we estimated the infection risk for unvaccinated children using published serological and surveillance data. Next, we derived infection risk for vaccinated children, assuming VE against infection of 57%. Uncorrected VE from 14 to 270 days post-vaccination was estimated from hospitalized children. We calculated the rate of depletion of susceptibles given infection risk and VE corrected for depletion-of-susceptibles bias. Waning rates for uncorrected and bias-corrected VE were measured by comparing VE at day 270 versus day 14. Bias was assessed as the absolute difference between two waning rates in percentage points. Waning rate of uncorrected VE was overestimated by 5.9 percentage points or 1.3 percentage points when assessed up to day 120. Bias was substantial when assuming 80% unvaccinated, and all vaccinated children were initially uninfected, but minimal when these proportions were similar. The observed waning in 2012/2013 was unlikely due to depletion-of-susceptibles bias. Further studies across various conditions are needed to confirm our findings.

We consider the problem of estimating fractional processes based on noisy high-frequency data. Generalizing the idea of pre-averaging to a fractional setting, we exhibit a sequence of consistent estimators for the unknown parameters of interest by proving a law of large numbers for associated variation functionals. In contrast to the semimartingale setting, the optimal window size for pre-averaging depends on the unknown roughness parameter of the underlying process. We evaluate the performance of our estimators in a simulation study and use them to empirically verify Kolmogorov’s $2/3$-law in turbulence data contaminated by instrument noise.

Let $\{X_{i}\}_{i\geq1}$ be a sequence of independent and identically distributed random variables and $T\in\{1,2,\ldots\}$ a stopping time associated with this sequence. In this paper, the distribution of the minimum observation, $\min\{X_{1},X_{2},\ldots,X_{T}\}$, until the stopping time T is provided by proposing a methodology based on an appropriate change of the initial probability measure of the probability space to a truncated (shifted) one on the $X_{i}$. As an application of the aforementioned general result, the random variables $X_{1},X_{2},\ldots$ are considered to be the interarrival times (spacings) between successive appearances of events in a renewal counting process $\{Y_{t},t\geq0\}$, while the stopping time T is set to be the number of summands until the sum of the $X_{i}$ exceeds t for the first time, i.e. $T=Y_{t}+1$. Under this setup, the distribution of the minimal spacing, $D_{t}=\min\{X_{1},X_{2},\ldots,X_{Y_{t}+1}\}$, that starts in the interval [0, t] is investigated and a stochastic ordering relation for $D_{t}$ is obtained. In addition, bounds for the tail probability of $D_{t}$ are provided when the interarrival times have the increasing failure rate / decreasing failure rate property. In the special case of a Poisson process, an exact formula, as well as closed-form bounds and an asymptotic result, are derived for the tail probability of $D_{t}$. Furthermore, for renewal processes with Erlang and uniformly distributed interarrival times, exact and approximation formulae for the tail probability of $D_{t}$ are also proposed. Finally, numerical examples are presented to illustrate the aforementioned exact and asymptotic results, and practical applications are briefly discussed.

Fitting loss distributions in insurance is sometimes a dilemma: either you get a good fit for the small/medium losses or for the very large losses. To be able to get both at the same time, this paper studies generalisations and extensions of the Pareto model that initially look like, for example, the Lognormal distribution but have a Pareto or GPD tail. We design a classification of such spliced distributions, which embraces and generalises various existing approaches. Special attention is paid to the geometry of distribution functions and to intuitive interpretations of the parameters, which can ease parameter inference from scarce data. The developed framework gives also new insights into the old Riebesell (power curve) exposure rating method.

We investigate a specific class of irreducible, level-dependent, discrete-time, GI/M/1-type Markov chains. The transition matrices possess a block lower-Hessenberg structure, which shows asymptotic convergence along the rows as the level approaches infinity. Criteria are presented for recurrence, transience, positive recurrence, geometric ergodicity, and geometric transience in terms of elements of the transition matrices. These criteria are established by employing drift functions and matrix-generating functions. Furthermore, we discuss the extension of the main results to the continuous-time case.

Societal challenges such as climate change and health inequalities require complex policy decisions, for which governmental organizations rely on a good information position. Having access to data from various domains is seen as a facilitator of making evidence-informed decisions that are more legitimate and less uncertain. To identify and make data available that is stored at various organizations, stakeholders participate in sociotechnical networks, also known as data ecosystems. Data ecosystems aimed at addressing societal challenges are characterized as complex because knowledge about societal issues is uncertain, information is scattered among (governmental) actors, collaboration extends beyond existing organizational networks, and values and interests of network actors can be conflicting. In this translational article, we examine how to successfully establish and maintain data ecosystems aimed at addressing societal challenges, given these complexities. We analyze two cases of successful data ecosystems in the Netherlands and present five narratives about how these data ecosystems navigated these complexities. We find that establishing collaboration among network actors, using bottom-up approaches, contributed to the success of both cases. The cases created structures in which participants were able prioritize the right questions, find common interests, and work together. The narratives present insights for government officials about collaboration in data ecosystems and add to the literature by highlighting the importance of organizational capabilities.

We investigate the asymptotic behavior of nearly unstable Hawkes processes whose regression kernel has $L^1$ norm strictly greater than 1 and close to 1 as time goes to infinity. We find that the scaling size determines the scaling behavior of the processes as in Jaisson and Rosenbaum (2015). Specifically, after a suitable rescale of $({a_T-1})/{T{\textrm{e}}^{b_TTx}}$, the limit of the sequence of Hawkes processes is deterministic. Also, with another appropriate rescaling of $1/T^2$, the sequence converges in law to an integrated Cox–Ingersoll–Ross-like process. This theoretical result may apply to model the recent COVID-19 outbreak in epidemiology and phenomena in social networks.

This paper presents the development of a graph autoencoder architecture capable of performing projection-based model-order reduction (PMOR) using a nonlinear manifold least-squares Petrov–Galerkin (LSPG) projection scheme. The architecture is particularly useful for advection-dominated flows modeled by unstructured meshes, as it provides a robust nonlinear mapping that can be leveraged in a PMOR setting. The presented graph autoencoder is constructed with a two-part process that consists of (1) generating a hierarchy of reduced graphs to emulate the compressive abilities of convolutional neural networks (CNNs) and (2) training a message passing operation at each step in the hierarchy of reduced graphs to emulate the filtering process of a CNN. The resulting framework provides improved flexibility over traditional CNN-based autoencoders because it is readily extendable to unstructured meshes. We provide an analysis of the interpretability of the graph autoencoder’s latent state variables, where we find that the Jacobian of the decoder for the proposed graph autoencoder provides interpretable mode shapes akin to traditional proper orthogonal decomposition modes. To highlight the capabilities of the proposed framework, which is named geometric deep least-squares Petrov–Galerkin (GD-LSPG), we benchmark the method on a one-dimensional Burgers’ model with a structured mesh and demonstrate the flexibility of GD-LSPG by deploying it on two test cases for two-dimensional Euler equations that use an unstructured mesh. The proposed framework is more flexible than using a traditional CNN-based autoencoder and provides considerable improvement in accuracy for very low-dimensional latent spaces in comparison with traditional affine projections.

This article proposes a local projection (LP) residual bootstrap method to construct confidence intervals for impulse response coefficients of AR(1) models. Our bootstrap method is based on the LP approach and involves a residual bootstrap procedure applied to AR(1) models. We present theoretical results for our bootstrap method and proposed confidence intervals. First, we prove the uniform consistency of the LP-residual bootstrap over a large class of AR(1) models that allow for a unit root, conditional heteroskedasticity of unknown form, and martingale difference shocks. Then, we prove the asymptotic validity of our confidence intervals over the same class of AR(1) models. Finally, we show that the LP-residual bootstrap provides asymptotic refinements for confidence intervals on a restricted class of AR(1) models relative to those required for the uniform consistency of our bootstrap.

This paper presents a comprehensive analysis of the frequency and severity of accidents involving electric vehicles (EVs) in comparison to internal combustion engine vehicles (ICEVs). It draws on extensive data from Norway from 2020 to 2023, a period characterised by significant EV adoption. We examine over two million registered EVs that collectively account for 28 billion kilometres of travel. In total we have analysed 139 billion kilometres of travel and close to 14,0000 accidents across all fuel types. We supplement this data with data from the Highway Loss Data Institute in the US and Association of British Insurers data in the UK as well as information from the Guy Carpenter large loss motor database.

A thorough analysis comparing accident frequency and severity of EVs with ICEVs in the literature to date has yet to be conducted, which this paper aims to address. This research will assist actuaries and analysts across various domains, including pricing, reserving and reinsurance considerations.

Our findings reveal a notable reduction in the frequency of accidents across all fuel types over time. Specifically, EVs demonstrate a lower accident frequency compared to ICEVs, a trend that may be attributed more to advancements in technology rather than the inherent characteristics of the fuel type, even when adjusted for COVID. Furthermore, our analysis indicates that EVs experience fewer accidents involving single units relative to non-EV and suggests a decrease in driver error and superior performance on regular road types.

Reduction in EV accident frequency of 17% and a change in the distribution of average severity with higher damage costs and lower injury costs leading to an overall reduction of 11%

However, it is important to note that when accidents do occur, the number of units involved as a proxy for severity involving EVs is marginally higher than those involving ICEVs. The average claim cost profile for EVs changes significantly with property damage claims being more expensive and bodily injury claims being less expensive for EVs.

Overall, our research concludes that EVs present a lower risk profile compared to their ICEV counterparts, highlighting the evolving landscape of vehicle safety in the context of increasing EV utilisation.

We study two continuous-time, time-inconsistent problems for an individual who purchases life annuities and invests her wealth in a risky asset under the mean-variance criterion. In the first problem, the buyer may only purchase life annuities at a bounded, continuous rate, while in the second problem, the buyer may purchase any amount of life annuity income at any time, which results in a singular control problem. We find the individual’s time-consistent equilibrium control strategies explicitly for the two life-annuity problems by solving the corresponding extended Hamilton–Jacobi–Bellman systems of equations. We also discuss the effects of parameters on the equilibrium strategies of the two life-annuity problems.

Assessing systemic risk presents a significant challenge in finance and insurance, where conditional risk measures are essential for capturing contagion effects. This paper introduces two novel systemic risk measures – conditional interval value-at-risk (CoIVaR) and conditional interval expected shortfall (CoIES) – which extend traditional metrics by incorporating interval-based uncertainty. A formal theoretical framework is developed for both measures, offering a detailed characterization of their key properties and risk contributions. We then propose a comprehensive comparison methodology for systemic risk assessment, leveraging stochastic orders, dependence structures, and marginal distributions to establish conditions for ranking risk vectors. Finally, through numerical experiments and real-world stock market applications, we demonstrate the practical utility of CoIVaR and CoIES in quantifying systemic risk under uncertainty. The findings provide valuable insights into systemic risk propagation and establish a robust foundation for risk management in interconnected financial systems.

Low-dimensional representation and clustering of network data are tasks of great interest across various fields. Latent position models are routinely used for this purpose by assuming that each node has a location in a low-dimensional latent space and by enabling node clustering. However, these models fall short through their inability to simultaneously determine the latent space dimension and number of clusters. Here we introduce the latent shrinkage position cluster model (LSPCM), which addresses this limitation. The LSPCM posits an infinite-dimensional latent space and assumes a Bayesian nonparametric shrinkage prior on the latent positions’ variance parameters resulting in higher dimensions having increasingly smaller variances, aiding the identification of dimensions with non-negligible variance. Further, the LSPCM assumes the latent positions follow a sparse finite Gaussian mixture model, allowing for automatic inference on the number of clusters related to non-empty mixture components. As a result, the LSPCM simultaneously infers the effective dimension of the latent space and the number of clusters, eliminating the need to fit and compare multiple models. The performance of the LSPCM is assessed via simulation studies and demonstrated through application to two real Twitter network datasets from sporting and political contexts. Open-source software is available to facilitate widespread use of the LSPCM.

Effectively controlling systems governed by partial differential equations (PDEs) is crucial in several fields of applied sciences and engineering. These systems usually yield significant challenges to conventional control schemes due to their nonlinear dynamics, partial observability, high-dimensionality once discretized, distributed nature, and the requirement for low-latency feedback control. Reinforcement learning (RL), particularly deep RL (DRL), has recently emerged as a promising control paradigm for such systems, demonstrating exceptional capabilities in managing high-dimensional, nonlinear dynamics. However, DRL faces challenges, including sample inefficiency, robustness issues, and an overall lack of interpretability. To address these challenges, we propose a data-efficient, interpretable, and scalable Dyna-style model-based RL framework specifically tailored for PDE control. Our approach integrates Sparse Identification of Nonlinear Dynamics with Control within an Autoencoder-based dimensionality reduction scheme for PDE states and actions (AE+SINDy-C). This combination enables fast rollouts with significantly fewer environment interactions while providing an interpretable latent space representation of the PDE dynamics, facilitating insight into the control process. We validate our method on two PDE problems describing fluid flows—namely, the 1D Burgers equation and 2D Navier–Stokes equations—comparing it against a model-free baseline. Our extensive analysis highlights improved sample efficiency, stability, and interpretability in controlling complex PDE systems.

We propose a one-to-many matching estimator of the average treatment effect based on propensity scores estimated by isotonic regression. This approach is predicated on the assumption of monotonicity in the propensity score function, a condition that can be justified in many economic applications. We show that the nature of the isotonic estimator can help us to fix many problems of existing matching methods, including efficiency, choice of the number of matches, choice of tuning parameters, robustness to propensity score misspecification, and bootstrap validity. As a by-product, a uniformly consistent isotonic estimator is developed for our proposed matching method.

We consider an inhomogeneous Erdős–Rényi random graph ensemble with exponentially decaying random disconnection probabilities determined by an independent and identically distributed field of variables with heavy tails and infinite mean associated with the vertices of the graph. This model was recently investigated in the physics literature (Garuccio, Lalli, and Garlaschelli 2023) as a scale-invariant random graph within the context of network renormalization. From a mathematical perspective, the model fits in the class of scale-free inhomogeneous random graphs whose asymptotic geometrical features have recently attracted interest. While for this type of graph several results are known when the underlying vertex variables have finite mean and variance, here instead we consider the case of one-sided stable variables with necessarily infinite mean. To simplify our analysis, we assume that the variables are sampled from a Pareto distribution with parameter $\alpha\in(0,1)$. We start by characterizing the asymptotic distributions of the typical degrees and some related observables. In particular, we show that the degree of a vertex converges in distribution, after proper scaling, to a mixed Poisson law. We then show that correlations among degrees of different vertices are asymptotically non-vanishing, but at the same time a form of asymptotic tail independence is found when looking at the behavior of the joint Laplace transform around zero. Moreover, we present some findings concerning the asymptotic density of wedges and triangles, and show a cross-over for the existence of dust (i.e. disconnected vertices).

The use of large language models (LLMs) has exploded since November 2022, but there is sparse evidence regarding LLM use in health, medical, and research contexts. We aimed to summarise the current uses of and attitudes towards LLMs across our campus’ clinical, research, and teaching sites. We administered a survey about LLM uses and attitudes. We conducted summary quantitative analysis and inductive qualitative analysis of free text responses. In August–September 2023, we circulated the survey amongst all staff and students across our three campus sites (approximately n = 7500), comprising a paediatric academic hospital, research institute, and paediatric university department. We received 281 anonymous survey responses. We asked about participants’ knowledge of LLMs, their current use of LLMs in professional or learning contexts, and perspectives on possible future uses, opportunities, and risks of LLM use. Over 90% of respondents have heard of LLM tools and about two-thirds have used them in their work on our campus. Respondents reported using LLMs for various uses, including generating or editing text and exploring ideas. Many, but not necessarily all, respondents seem aware of the limitations and potential risks of LLMs, including privacy and security risks. Various respondents expressed enthusiasm about the opportunities of LLM use, including increased efficiency. Our findings show LLM tools are already widely used on our campus. Guidelines and governance are needed to keep up with practice. Insights from this survey were used to develop recommendations for the use of LLMs on our campus.

Inference and prediction under partial knowledge of a physical system is challenging, particularly when multiple confounding sources influence the measured response. Explicitly accounting for these influences in physics-based models is often infeasible due to epistemic uncertainty, cost, or time constraints, resulting in models that fail to accurately describe the behavior of the system. On the other hand, data-driven machine learning models such as variational autoencoders are not guaranteed to identify a parsimonious representation. As a result, they can suffer from poor generalization performance and reconstruction accuracy in the regime of limited and noisy data. We propose a physics-informed variational autoencoder architecture that combines the interpretability of physics-based models with the flexibility of data-driven models. To promote disentanglement of the known physics and confounding influences, the latent space is partitioned into physically meaningful variables that parametrize a physics-based model, and data-driven variables that capture variability in the domain and class of the physical system. The encoder is coupled with a decoder that integrates physics-based and data-driven components, and constrained by an adversarial training objective that prevents the data-driven components from overriding the known physics, ensuring that the physics-grounded latent variables remain interpretable. We demonstrate that the model is able to disentangle features of the input signal and separate the known physics from confounding influences using supervision in the form of class and domain observables. The model is evaluated on a series of synthetic case studies relevant to engineering structures, demonstrating the feasibility of the proposed approach.