Globally, countries have used diverse methods to report data during the COVID-19 pandemic. Using international guidelines and principles of emergency management, we compare national data reporting systems in African countries in order to determine lessons for future pandemics. We analyse COVID-19 reporting practices across 54 African countries through 2020. Reporting systems were diverse and included summaries, press releases, situation reports and online dashboards. These systems were communicated via social media accounts and websites belonging to ministries of health and public health. Data variables from the reports included event detection (cases/deaths/recoveries), risk assessment (demographics/co-morbidities) and response (total tests/hospitalisations). Of countries with reporting systems, 36/53 (67.9%) had recurrent situation reports and/or online dashboards which provided more extensive data. All of these systems reported cases, deaths and recoveries. However, few systems contained risk assessment and response data, with only 5/36 (13.9%) reporting patient co-morbidities and 9/36 (25%) including total hospitalisations. Further evaluation of reporting practices in Cameroon, Egypt, Kenya, Senegal and South Africa as examples from different sub-regions revealed differences in reporting healthcare capacity and preparedness data. Improving the standardisation and accessibility of national data reporting systems could augment research and decision-making, as well as increase public awareness and transparency for national governments.

Even within well-studied organisms, many genes lack useful functional annotations. One way to generate such functional information is to infer biological relationships between genes or proteins, using a network of gene coexpression data that includes functional annotations. Signed distance correlation has proved useful for the construction of unweighted gene coexpression networks. However, transforming correlation values into unweighted networks may lead to a loss of important biological information related to the intensity of the correlation. Here, we introduce a principled method to construct weighted gene coexpression networks using signed distance correlation. These networks contain weighted edges only between those pairs of genes whose correlation value is higher than a given threshold. We analyze data from different organisms and find that networks generated with our method based on signed distance correlation are more stable and capture more biological information compared to networks obtained from Pearson correlation. Moreover, we show that signed distance correlation networks capture more biological information than unweighted networks based on the same metric. While we use biological data sets to illustrate the method, the approach is general and can be used to construct networks in other domains. Code and data are available on https://github.com/javier-pardodiaz/sdcorGCN.

Survivor funds are financial arrangements where participants agree to share the proceeds of a collective investment pool in a predescribed way depending on their survival. This offers investors a way to benefit from mortality credits, boosting financial returns. Following Denuit (2019, ASTIN Bulletin, 49, 591–617), participants are assumed to adopt the conditional mean risk sharing rule introduced in Denuit and Dhaene (2012, Insurance: Mathematics and Economics, 51, 265–270) to assess their respective shares in mortality credits. This paper looks at pools of individuals that are heterogeneous in terms of their survival probability and their contributions. Imposing mild conditions, we show that individual risk can be fully diversified if the size of the group tends to infinity. For large groups, we derive simple, hierarchical approximations of the conditional mean risk sharing rule.

In this article we consider a Monte-Carlo-based method to filter partially observed diffusions observed at regular and discrete times. Given access only to Euler discretizations of the diffusion process, we present a new procedure which can return online estimates of the filtering distribution with no time-discretization bias and finite variance. Our approach is based upon a novel double application of the randomization methods of Rhee and Glynn (Operat. Res. 63, 2015) along with the multilevel particle filter (MLPF) approach of Jasra et al. (SIAM J. Numer. Anal. 55, 2017). A numerical comparison of our new approach with the MLPF, on a single processor, shows that similar errors are possible for a mild increase in computational cost. However, the new method scales strongly to arbitrarily many processors.

We consider the spectral analysis of several examples of bilateral birth–death processes and compute explicitly the spectral matrix and the corresponding orthogonal polynomials. We also use the spectral representation to study some probabilistic properties of the processes, such as recurrence, the invariant distribution (if it exists), and the probability current.

We propose non-asymptotic controls of the cumulative distribution function $\mathbb{P}(|X_{t}|\ge \varepsilon)$, for any $t>0$, $\varepsilon>0$ and any Lévy process X such that its Lévy density is bounded from above by the density of an $\alpha$-stable-type Lévy process in a neighborhood of the origin.

Using data from 20 years of Salmonella foodborne outbreaks, this study investigates significant trends in the proportion of outbreaks associated with 12 broad commodity groups. Outbreak counts are demonstrated to have a stronger trend signal than outbreak illness counts. The number of outbreaks with an identified food vehicle increased significantly between 1998 and 2000. This was followed by a 10-year period when the number of outbreaks decreased. The number of outbreaks increased significantly between 2010 and 2014 and then remained unchanged for the remainder of the study period. During the period of 1998 through 2017, the proportion of outbreaks for three commodities groups, consisting of eggs, pork and seeded vegetables, changed significantly. No significant changes were observed in the remaining nine commodity groups. Simple approximations are derived to highlight the effect of dependencies between outbreak proportions and a consumption analysis for meat and poultry is used to enhance the limited interpretability of the changes in these proportions. Given commodity-specific approaches to verifying food safety and promoting pathogen reduction, regulatory agencies benefit from analyses that elucidate illness trends attributable to the products under their jurisdiction. Results from this trend analysis can be used to inform the development and assessment of new pathogen reduction programmes in the United States.

We establish sufficient conditions for differentiability of the expected cost collected over a discrete-time Markov chain until it enters a given set. The parameter with respect to which differentiability is analysed may simultaneously affect the Markov chain and the set defining the stopping criterion. The general statements on differentiability lead to unbiased gradient estimators.

Bifurcating Markov chains (BMCs) are Markov chains indexed by a full binary tree representing the evolution of a trait along a population where each individual has two children. We provide a central limit theorem for additive functionals of BMCs under $L^2$-ergodic conditions with three different regimes. This completes the pointwise approach developed in a previous work. As an application, we study the elementary case of a symmetric bifurcating autoregressive process, which justifies the nontrivial hypothesis considered on the kernel transition of the BMCs. We illustrate in this example the phase transition observed in the fluctuations.

Empirical studies (e.g. Jiang et al. (2015) and Mislove et al. (2007)) show that online social networks have not only in- and out-degree distributions with Pareto-like tails, but also a high proportion of reciprocal edges. A classical directed preferential attachment (PA) model generates in- and out-degree distributions with power-law tails, but the theoretical properties of the reciprocity feature in this model have not yet been studied. We derive asymptotic results on the number of reciprocal edges between two fixed nodes, as well as the proportion of reciprocal edges in the entire PA network. We see that with certain choices of parameters, the proportion of reciprocal edges in a directed PA network is close to 0, which differs from the empirical observation. This points out one potential problem of fitting a classical PA model to a given network dataset with high reciprocity, and indicates that alternative models need to be considered.

In this paper we propose a general framework for modeling an insurance liability cash flow in continuous time, by generalizing the reduced-form framework for credit risk and life insurance. In particular, we assume a nontrivial dependence structure between the reference filtration and the insurance internal filtration. We apply these results for pricing and hedging non-life insurance liabilities in hybrid financial and insurance markets, while taking into account the role of inflation under the benchmarked risk-minimization approach. This framework offers at the same time a general and flexible structure, and an explicit and treatable pricing-hedging formula.

We study the integrated telegraph process $X_t$ under the assumption of general distribution for the random times between consecutive reversals of direction. Specifically, $X_t$ represents the position, at time t, of a particle moving U time units upwards with velocity c and D time units downwards with velocity $-c$. The latter motions are repeated cyclically, according to independent alternating renewals. Explicit expressions for the probability law of $X_t$ are given in the following cases: (i) (U, D) gamma-distributed; (ii) U exponentially distributed and D gamma-distributed. For certain values of the parameters involved, the probability law of $X_t$ is provided in a closed form. Some expressions for the moment generating function of $X_t$ and its Laplace transform are also obtained. The latter allows us to prove the existence of a Kac-type condition under which the probability density function of the integrated telegraph process, with identically distributed gamma intertimes, converges to that of the standard Brownian motion.

Finally, we consider the square of $X_t$ and disclose its distribution function, specifying the expression for some choices of the distribution of (U, D).

We apply general moment identities for Poisson stochastic integrals with random integrands to the computation of the moments of Markovian growth–collapse processes. This extends existing formulas for mean and variance available in the literature to closed-form moment expressions of all orders. In comparison with other methods based on differential equations, our approach yields explicit summations in terms of the time parameter. We also treat the case of the associated embedded chain, and provide recursive codes in Maple and Mathematica for the computation of moments and cumulants of any order with arbitrary cut-off moment sequences and jump size functions.

We consider residue expansions for survival and density/mass functions of first-passage distributions in finite-state semi-Markov processes (SMPs) in continuous and integer time. Conditions are given which guarantee that the residue expansions for these functions have a dominant exponential/geometric term. The key condition assumes that the relevant states for first passage contain an irreducible class, thus ensuring the same sort of dominant exponential/geometric terms as one gets for phase-type distributions in Markov processes. Essentially, the presence of an irreducible class along with some other conditions ensures that the boundary singularity b for the moment generating function (MGF) of the first-passage-time distribution is a simple pole. In the continuous-time setting we prove that b is a dominant pole, in that the MGF has no other pole on the vertical line $\{\text{Re}(s)=b\}.$ In integer time we prove that b is dominant if all holding-time mass functions for the SMP are aperiodic and non-degenerate. The expansions and pole characterisations address first passage to a single new state or a subset of new states, and first return to the starting state. Numerical examples demonstrate that the residue expansions are considerably more accurate than saddlepoint approximations and can provide a substitute for exact computation above the 75th percentile.

We study an intertemporal consumption and portfolio choice problem under Knightian uncertainty in which agent’s preferences exhibit local intertemporal substitution. We also allow for market frictions in the sense that the pricing functional is nonlinear. We prove existence and uniqueness of the optimal consumption plan, and we derive a set of sufficient first-order conditions for optimality. With the help of a backward equation, we are able to determine the structure of optimal consumption plans. We obtain explicit solutions in a stationary setting in which the financial market has different risk premia for short and long positions.

We consider two-dimensional Lévy processes reflected to stay in the positive quadrant. Our focus is on the non-standard regime when the mean of the free process is negative but the reflection vectors point away from the origin, so that the reflected process escapes to infinity along one of the axes. Under rather general conditions, it is shown that such behaviour is certain and each component can dominate the other with positive probability for any given starting position. Additionally, we establish the corresponding invariance principle providing justification for the use of the reflected Brownian motion as an approximate model. Focusing on the probability that the first component dominates, we derive a kernel equation for the respective Laplace transform in the starting position. This is done for the compound Poisson model with negative exponential jumps and, by means of approximation, for the Brownian model. Both equations are solved via boundary value problem analysis, which also yields the domination probability when starting at the origin. Finally, certain asymptotic analysis and numerical results are presented.

This paper introduces a counting process for event arrivals in high-frequency trading, based on high-dimensional covariates. The novelty is that, under sparsity conditions on the true model, we do not need to impose any model penalty or parameters shrinkage, unlike Lasso. The procedure allows us to derive a central limit theorem to test restrictions in a two-stage estimator. We achieve this by the use of a sign constraint on the intensity which necessarily needs to be positive. In particular, we introduce an additive model to extract the nonlinear impact of order book variables on buy and sell trade arrivals. In the empirical application, we show that the shape and dynamics of the order book are fundamental in determining the arrival of buy and sell trades in the crude oil futures market. We establish our empirical results mapping the covariates into a higher-dimensional space. Consistently with the theoretical results, the estimated models are sparse in the number of parameters. Using this approach, we are also able to compare competing model hypotheses on the basis of an out-of-sample likelihood ratio type of test.

Restless bandits are a class of sequential resource allocation problems concerned with allocating one or more resources among several alternative processes where the evolution of the processes depends on the resources allocated to them. Such models capture the fundamental trade-offs between exploration and exploitation. In 1988, Whittle developed an index heuristic for restless bandit problems which has emerged as a popular solution approach because of its simplicity and strong empirical performance. The Whittle index heuristic is applicable if the model satisfies a technical condition known as indexability. In this paper, we present two general sufficient conditions for indexability and identify simpler-to-verify refinements of these conditions. We then revisit a previously proposed algorithm called the adaptive greedy algorithm which is known to compute the Whittle index for a sub-class of restless bandits. We show that a generalization of the adaptive greedy algorithm computes the Whittle index for all indexable restless bandits. We present an efficient implementation of this algorithm which can compute the Whittle index of a restless bandit with K states in $\mathcal{O}\!\left(K^3\right)$ computations. Finally, we present a detailed numerical study which affirms the strong performance of the Whittle index heuristic.

This article applies a knowledge graph-based approach to unify multiple heterogeneous domains inherent in climate and energy supply research. Existing approaches that rely on bespoke models with spreadsheet-type inputs are noninterpretable, static and make it difficult to combine existing domain specific models. The difficulties inherent to this approach become increasingly prevalent as energy supply models gain complexity while society pursues a net-zero future. In this work, we develop new ontologies to extend the World Avatar knowledge graph to represent gas grids, gas consumption statistics, and climate data. Using a combination of the new and existing ontologies we construct a Universal Digital Twin that integrates data describing the systems of interest and specifies respective links between domains. We represent the UK gas transmission system, and HadUK-Grid climate data set as linked data for the first time, formally associating the data with the statistical output areas used to report governmental administrative data throughout the UK. We demonstrate how computational agents contained within the World Avatar can operate on the knowledge graph, incorporating live feeds of data such as instantaneous gas flow rates, as well as parsing information into interpretable forms such as interactive visualizations. Through this approach, we enable a dynamic, interpretable, modular, and cross-domain representation of the UK that enables domain specific experts to contribute toward a national-scale digital twin.