In this paper we study the asymptotic behaviour of a random uniform parking function $\pi_n$ of size n. We show that the first $k_n$ places $\pi_n(1),\ldots,\pi_n(k_n)$ of $\pi_n$ are asymptotically independent and identically distributed (i.i.d.) and uniform on $\{1,2,\ldots,n\}$, for the total variation distance when $k_n = {\rm{o}}(\sqrt{n})$, and for the Kolmogorov distance when $k_n={\rm{o}}(n)$, improving results of Diaconis and Hicks. Moreover, we give bounds for the rate of convergence, as well as limit theorems for certain statistics such as the sum or the maximum of the first $k_n$ parking places. The main tool is a reformulation using conditioned random walks.

When subjected to a sudden, unanticipated threat, human groups characteristically self-organize to identify the threat, determine potential responses, and act to reduce its impact. Central to this process is the challenge of coordinating information sharing and response activity within a disrupted environment. In this paper, we consider coordination in the context of responses to the 2001 World Trade Center (WTC) disaster. Using records of communications among 17 organizational units, we examine the mechanisms driving communication dynamics, with an emphasis on the emergence of coordinating roles. We employ relational event models (REMs) to identify the mechanisms shaping communications in each unit, finding a consistent pattern of behavior across units with very different characteristics. Using a simulation-based “knock-out” study, we also probe the importance of different mechanisms for hub formation. Our results suggest that, while preferential attachment and pre-disaster role structure generally contribute to the emergence of hub structure, temporally local conversational norms play a much larger role in the WTC case. We discuss broader implications for the role of microdynamics in driving macroscopic outcomes, and for the emergence of coordination in other settings.

We investigated cardiovascular disease (CVD) risk associated with latent tuberculosis infection (LTBI) (Aim-1) and LTBI therapy (Aim-2) in British Columbia, a low-tuberculosis-incidence setting. 49,197 participants had valid LTBI test results. Cox proportional hazards model was fitted, adjusting for potential confounders. Compared with the participants who tested LTBI negative, LTBI positive was associated with an 8% higher CVD risk in complete case data (adjusted hazard ratio (HR): 1.08, 95% CI: 0.99-1.18), a statistically significant 11% higher risk when missing confounder values were imputed using multiple imputation (HR: 1.11, 95% CI: 1.02-1.20), and 10% higher risk when additional proxy variables supplementing known unmeasured confounders were incorporated in the highdimensional disease risk score technique to reduce residual confounding (HR: 1.10, 95% CI: 1.01-1.20). Also, compared with participants who tested negative, CVD risk was 27% higher among people who were LTBI positive but incomplete LTBI therapy (HR: 1.27, 95% CI: 1.04-1.55), whereas the risk was similar in people who completed LTBI therapy (HR: 1.04, 95% CI: 0.87-1.24). Findings were consistent in different sensitivity analyses. We concluded that LTBI is associated with an increased CVD risk in low-tuberculosis-incidence settings, with a higher risk associated with incomplete LTBI therapy and attenuated risk when therapy is completed.

The global and uneven spread of COVID-19, mirrored at the local scale, reveals stark differences along racial and ethnic lines. We respond to the pressing need to understand these divergent outcomes via neighborhood level analysis of mobility and case count information. Using data from Chicago over 2020, we leverage a metapopulation Susceptible-Exposed-Infectious-Removed model to reconstruct and simulate the spread of SARS-CoV-2 at the ZIP Code level. We demonstrate that exposures are mostly contained within one’s own ZIP Code and demographic group. Building on this observation, we illustrate that we can understand epidemic progression using a composite metric combining the volume of mobility and the risk that each trip represents, while separately these factors fail to explain the observed heterogeneity in neighborhood level outcomes. Having established this result, we next uncover how group level differences in these factors give rise to disparities in case rates along racial and ethnic lines. Following this, we ask what-if questions to quantify how segregation impacts COVID-19 case rates via altering mobility patterns. We find that segregation in the mobility network has contributed to inequality in case rates across demographic groups.

The International Maritime Organization along with couple European countries (Paris MoU) has introduced in 1982 the port state control (PSC) inspections of vessels in national ports to evaluate their compliance with safety and security regulations. This study discusses how the PSC data share common characteristics with Big Data fundamental theories, and by interpreting them as Big Data, we could enjoy their governance and transparency as a Big Data challenge to gain value from their use. Thus, from the scope of Big Data, PSC should exhibit volume, velocity, variety, value, and complexity to support in the best possible way both officers ashore and on board to maintain the vessel in the best possible conditions for sailing. For the above purpose, this paper employs Big Data theories broadly used within the academic and business environment on datasets characteristics and how to access the value from Big Data and Analytics. The research concludes that PSC data provide valid information to the shipping industry. However, the lack of PSC data ability to present the complete picture of PSC regimes and ports challenges the maritime community’s attempts for a safer and more sustainable industry.

We introduce a new test for a two-sided hypothesis involving a subset of the structural parameter vector in the linear instrumental variables (IVs) model. Guggenberger, Kleibergen, and Mavroeidis (2019, Quantitative Economics, 10, 487–526; hereafter GKM19) introduce a subvector Anderson–Rubin (AR) test with data-dependent critical values that has asymptotic size equal to nominal size for a parameter space that allows for arbitrary strength or weakness of the IVs and has uniformly nonsmaller power than the projected AR test studied in Guggenberger et al. (2012, Econometrica, 80(6), 2649–2666). However, GKM19 imposes the restrictive assumption of conditional homoskedasticity (CHOM). The main contribution here is to robustify the procedure in GKM19 to arbitrary forms of conditional heteroskedasticity. We first adapt the method in GKM19 to a setup where a certain covariance matrix has an approximate Kronecker product (AKP) structure which nests CHOM. The new test equals this adaptation when the data are consistent with AKP structure as decided by a model selection procedure. Otherwise, the test equals the AR/AR test in Andrews (2017, Identification-Robust Subvector Inference, Cowles Foundation Discussion Papers 3005, Yale University) that is fully robust to conditional heteroskedasticity but less powerful than the adapted method. We show theoretically that the new test has asymptotic size bounded by the nominal size and document improved power relative to the AR/AR test in a wide array of Monte Carlo simulations when the covariance matrix is not too far from AKP.

In deception research, little consideration is given to how the framing of the question might impact the decision-making process used to reach a veracity judgment. People use terms such as “sure” to describe their uncertainty about an event (i.e., aleatory) and terms such as “chance” to describe their uncertainty about the world (i.e., epistemic). Presently, the effect of such uncertainty framing on veracity judgments was considered. By manipulating the veracity question wording the effect of uncertainty framing on deception detection was measured. The data show no difference in veracity judgments between the two uncertainty framing conditions, suggesting that these may operate on a robust and invariant cognitive process.

Consider a set of n vertices, where each vertex has a location in $\mathbb{R}^d$ that is sampled uniformly from the unit cube in $\mathbb{R}^d$, and a weight associated to it. Construct a random graph by placing edges independently for each vertex pair with a probability that is a function of the distance between the locations and the vertex weights.

Under appropriate integrability assumptions on the edge probabilities that imply sparseness of the model, after appropriately blowing up the locations, we prove that the local limit of this random graph sequence is the (countably) infinite random graph on $\mathbb{R}^d$ with vertex locations given by a homogeneous Poisson point process, having weights which are independent and identically distributed copies of limiting vertex weights. Our set-up covers many sparse geometric random graph models from the literature, including geometric inhomogeneous random graphs (GIRGs), hyperbolic random graphs, continuum scale-free percolation, and weight-dependent random connection models.

We prove that the limiting degree distribution is mixed Poisson and the typical degree sequence is uniformly integrable, and we obtain convergence results on various measures of clustering in our graphs as a consequence of local convergence. Finally, as a byproduct of our argument, we prove a doubly logarithmic lower bound on typical distances in this general setting.

We investigated the potential effects of COVID-19 public health restrictions on the prevalence and distribution of Neisseria gonorrhoeae (NG) genotypes in our Queensland isolate population in the first half of the year 2020. A total of 763 NG isolates were genotyped to examine gonococcal strain distribution and prevalence for the first 6 months of 2020, with 1 January 2020 to 31 March 2020 classified as ‘pre’ COVID-19 restrictions (n = 463) and 1 April 2020 to 30 June 2020 classified as ‘post’ COVID-19 restrictions (n = 300). Genotypes most prevalent ‘pre’ restrictions remained proportionally high ‘post’ restrictions, with some significantly increasing ‘post’ restrictions. However, genotype diversity was significantly reduced ‘post’ restrictions. Overall, it seems public health restrictions (9–10 weeks) were not sufficient to affect rates of infection or reduce the prevalence of well-established genotypes in our population, potentially due to reduced access to services or health-seeking behaviours.

We construct a class of non-reversible Metropolis kernels as a multivariate extension of the guided-walk kernel proposed by Gustafson (Statist. Comput. 8, 1998). The main idea of our method is to introduce a projection that maps a state space to a totally ordered group. By using Haar measure, we construct a novel Markov kernel termed the Haar mixture kernel, which is of interest in its own right. This is achieved by inducing a topological structure to the totally ordered group. Our proposed method, the $\Delta$-guided Metropolis–Haar kernel, is constructed by using the Haar mixture kernel as a proposal kernel. The proposed non-reversible kernel is at least 10 times better than the random-walk Metropolis kernel and Hamiltonian Monte Carlo kernel for the logistic regression and a discretely observed stochastic process in terms of effective sample size per second.

The paper is concerned with common shock models of claim triangles. These are usually constructed as linear combinations of shock components and idiosyncratic components. Previous literature has discussed the unbalanced property of such models, whereby the shocks may over- or under-contribute to some observations. The literature has also introduced corrections for this. The present paper discusses “auto-balanced” models, in which all shock and idiosyncratic components contribute to observations such that their proportionate contributions are constant from one observation to another. The conditions for auto-balance are found to be simple and applicable to a wide range of model structures. Numerical illustrations are given.

An extension of Shannon’s entropy power inequality when one of the summands is Gaussian was provided by Costa in 1985, known as Costa’s concavity inequality. We consider the additive Gaussian noise channel with a more realistic assumption, i.e. the input and noise components are not independent and their dependence structure follows the well-known multivariate Gaussian copula. Two generalizations for the first- and second-order derivatives of the differential entropy of the output signal for dependent multivariate random variables are derived. It is shown that some previous results in the literature are particular versions of our results. Using these derivatives, concavity of the entropy power, under certain mild conditions, is proved. Finally, special one-dimensional versions of our general results are described which indeed reveal an extension of the one-dimensional case of Costa’s concavity inequality to the dependent case. An illustrative example is also presented.

Two ensembles are frequently used to model random graphs subject to constraints: the microcanonical ensemble (= hard constraint) and the canonical ensemble (= soft constraint). It is said that breaking of ensemble equivalence (BEE) occurs when the specific relative entropy of the two ensembles does not vanish as the size of the graph tends to infinity. Various examples have been analysed in the literature. It was found that BEE is the rule rather than the exception for two classes of constraints: sparse random graphs when the number of constraints is of the order of the number of vertices, and dense random graphs when there are two or more constraints that are frustrated. We establish BEE for a third class: dense random graphs with a single constraint on the density of a given simple graph. We show that BEE occurs in a certain range of choices for the density and the number of edges of the simple graph, which we refer to as the BEE-phase. We also show that, in part of the BEE-phase, there is a gap between the scaling limits of the averages of the maximal eigenvalue of the adjacency matrix of the random graph under the two ensembles, a property that is referred to as the spectral signature of BEE. We further show that in the replica symmetric region of the BEE-phase, BEE is due to the coexistence of two densities in the canonical ensemble.

We consider a premium control problem in discrete time, formulated in terms of a Markov decision process. In a simplified setting, the optimal premium rule can be derived with dynamic programming methods. However, these classical methods are not feasible in a more realistic setting due to the dimension of the state space and lack of explicit expressions for transition probabilities. We explore reinforcement learning techniques, using function approximation, to solve the premium control problem for realistic stochastic models. We illustrate the appropriateness of the approximate optimal premium rule compared with the true optimal premium rule in a simplified setting and further demonstrate that the approximate optimal premium rule outperforms benchmark rules in more realistic settings where classical approaches fail.

In this study, we quantify the relationship between socio-economic status and life expectancy and identify combinations of socio-economic variables that are particularly useful for explaining mortality differences between neighbourhoods in England. We achieve this by examining socio-economic variation in mortality experiences across small areas in England known as lower layer super output areas (LSOAs). We then consider 12 socio-economic variables that are known to have a strong association with mortality. We estimate the relationship between those variables and mortality rates using a random forest algorithm. Based on the resulting estimate, we then create a new socio-economic mortality index – the Longevity Index for England (LIFE). The index is constructed in a way that eliminates the impact of care homes that might artificially increase mortality rates in LSOAs with care homes compared to LSOAs that do not contain a care home. Using mortality data for different age groups, we make the index age-dependent and investigate the impact of specific socio-economic characteristics on the age-specific mortality risk. We compare the explanatory power of the LIFE index to the English Index of Multiple Deprivation (IMD) as predictors of mortality. While we find that the IMD can explain regional mortality differences to some extent, the LIFE index has significantly greater explanatory power for mortality differences between regions. Our empirical results also indicate that income deprivation amongst the elderly and employment deprivation are the most significant socio-economic factors for explaining mortality variation across LSOAs in England.

Stein’s method is used to study discrete representations of multidimensional distributions that arise as approximations of states of quantum harmonic oscillators. These representations model how quantum effects result from the interaction of finitely many classical ‘worlds’, with the role of sample size played by the number of worlds. Each approximation arises as the ground state of a Hamiltonian involving a particular interworld potential function. Our approach, framed in terms of spherical coordinates, provides the rate of convergence of the discrete approximation to the ground state in terms of Wasserstein distance. Applying a novel Stein’s method technique to the radial component of the ground state solution, the fastest rate of convergence to the ground state is found to occur in three dimensions.