We study the noise sensitivity of the minimum spanning tree (MST) of the $n$-vertex complete graph when edges are assigned independent random weights. It is known that when the graph distance is rescaled by $n^{1/3}$ and vertices are given a uniform measure, the MST converges in distribution in the Gromov–Hausdorff–Prokhorov (GHP) topology. We prove that if the weight of each edge is resampled independently with probability $\varepsilon \gg n^{-1/3}$, then the pair of rescaled minimum spanning trees – before and after the noise – converges in distribution to independent random spaces. Conversely, if $\varepsilon \ll n^{-1/3}$, the GHP distance between the rescaled trees goes to $0$ in probability. This implies the noise sensitivity and stability for every property of the MST that corresponds to a continuity set of the random limit. The noise threshold of $n^{-1/3}$ coincides with the critical window of the Erdős-Rényi random graphs. In fact, these results follow from an analog theorem we prove regarding the minimum spanning forest of critical random graphs.

Information generating functions (IGFs) have been of great interest to researchers due to their ability to generate various information measures. The IGF of an absolutely continuous random variable (see Golomb, S. (1966). The information generating function of a probability distribution. IEEE Transactions in Information Theory, 12(1), 75–77) depends on its density function. But, there are several models with intractable cumulative distribution functions, but do have explicit quantile functions. For this reason, in this work, we propose quantile version of the IGF, and then explore some of its properties. Effect of increasing transformations on it is then studied. Bounds are also obtained. The proposed generating function is studied especially for escort and generalized escort distributions. Some connections between the quantile-based IGF (Q-IGF) order and well-known stochastic orders are established. Finally, the proposed Q-IGF is extended for residual and past lifetimes as well. Several examples are presented through out to illustrate the theoretical results established here. An inferential application of the proposed methodology is also discussed

Let $\mathcal{V}$ and $\mathcal{U}$ be the point sets of two independent homogeneous Poisson processes on $\mathbb{R}^d$. A graph $\mathcal{G}_\mathcal{V}$ with vertex set $\mathcal{V}$ is constructed by first connecting pairs of points (v, u) with $v\in\mathcal{V}$ and $u\in\mathcal{U}$ independently with probability $g(v-u)$, where g is a non-increasing radial function, and then connecting two points $v_1,v_2\in\mathcal{V}$ if and only if they have a joint neighbor $u\in\mathcal{U}$. This gives rise to a random intersection graph on $\mathbb{R}^d$. Local properties of the graph, including the degree distribution, are investigated and quantified in terms of the intensities of the underlying Poisson processes and the function g. Furthermore, the percolation properties of the graph are characterized and shown to differ depending on whether g has bounded or unbounded support.

Brucellosis, a global zoonosis, is endemic in Israel. We used a national database of culture-confirmed cases (2004–2022) to analyse the trends of brucellosis. Of 2,489 unique cases, 99.8% were bacteraemic, 64% involved males, and the mean age was 30.5 years. Brucella melitensis was the dominant species (99.6%). Most cases occurred among the Arab sector (84.9%) followed by the Jewish (8.5%) and Druze (5.5%) sectors. The average annual incidence rates overall and for the Arab, Druze, and Jewish sectors were 1.6/100,000, 6.6/100,000, 5.5/100,000, and 0.18/100,000, respectively. The annual incidence rates among the Arab (incidence rate ratio (IRR) = 36.4) and the Druze (IRR = 29.6) sectors were significantly higher than among the Jewish sector (p < 0.001). The highest incidence rates among the Arab sector occurred in the South District, peaking at 41.0/100,000 in 2012. The frequencies of B. melitensis isolated biotypes (biotype 1 – 69.1%, biotype 2 – 26.0%, and biotype 3 – 4.3%) differed from most Middle Eastern and European countries. A significant switch between the dominant biotypes was noted in the second half of the study period. Efforts for control and prevention should be sustained and guided by a One Health approach mindful of the differential trends and changing epidemiology.

There is mounting pressure on (re)insurers to quantify the impacts of climate change, notably on the frequency and severity of claims due to weather events such as flooding. This is however a very challenging task for (re)insurers as it requires modeling at the scale of a portfolio and at a high enough spatial resolution to incorporate local climate change effects. In this paper, we introduce a data science approach to climate change risk assessment of pluvial flooding for insurance portfolios over Canada and the United States (US). The underlying flood occurrence model quantifies the financial impacts of short-term (12–48 h) precipitation dynamics over the present (2010–2030) and future climate (2040–2060) by leveraging statistical/machine learning and regional climate models. The flood occurrence model is designed for applications that do not require street-level precision as is often the case for scenario and trend analyses. It is applied at the full scale of Canada and the US over 10–25 km grids. Our analyses show that climate change and urbanization will typically increase losses over Canada and the US, while impacts are strongly heterogeneous from one state or province to another, or even within a territory. Portfolio applications highlight the importance for a (re)insurer to differentiate between future changes in hazard and exposure, as the latter may magnify or attenuate the impacts of climate change on losses.

We analyzed data from a community-based acute respiratory illness study involving K-12 students and their families in southcentral Wisconsin and assessed household transmission of two common seasonal respiratory viruses – human metapneumovirus (HMPV) and human coronaviruses OC43 and HKU1 (HCOV). We found secondary infection rates of 12.2% (95% CI: 8.1%–17.4%) and 19.2% (95% CI: 13.8%–25.7%) for HMPV and HCOV, respectively. We performed individual- and family-level regression models and found that HMPV transmission was positively associated age of the index case (individual model: p = .016; family model: p = .004) and HCOV transmission was positively associated with household density (family model: p = .048). We also found that the age of the non-index case was negatively associated with transmission of both HMPV (individual model: p = .049) and HCOV (individual model: p = .041), but we attributed this to selection bias from the original study design. Understanding household transmission of common respiratory viruses like HMPV and HCOV may help to broaden our understanding of the overall disease burden and establish methods to prevent the spread of disease from low- to high-risk populations.

Spatial autoregressive (SAR) and related models offer flexible yet parsimonious ways to model spatial and network interactions. SAR specifications typically rely on a particular parametric functional form and an exogenous choice of the so-called spatial weight matrix with only limited guidance from theory in making these specifications. Also, the choice of a SAR model over other alternatives, such as spatial Durbin (SD) or spatial lagged X (SLX) models, is often arbitrary, raising issues of potential specification error. To address such issues, this paper develops a new specification test within the SAR framework that can detect general forms of misspecification including that of the spatial weight matrix, the functional form and the model itself. The test is robust to the presence of heteroskedasticity of unknown form in the disturbances and the approach relates to the conditional moment test framework of Bierens ([1982, Journal of Econometrics 20, 105–134], [1990, Econometrica 58, 1443–1458]). The Bierens test is shown to be inconsistent in general against spatial alternatives and the new test introduces modifications to achieve test consistency in the spatial setting. A central element is the infinite-dimensional endogeneity induced by spatial linkages. This complexity is addressed by introducing a new component to the omnibus test that captures the effects of potential spatial matrix misspecification. With this modification, the approach leads to a simple pivotal test procedure with standard critical values that is the first test in the literature to have power against misspecifications in the spatial linkages. We derive the asymptotic distribution of the test under the null hypothesis of correct SAR specification and prove consistency. A Monte Carlo study is conducted to study its finite sample performance. An empirical illustration on the performance of the test in modeling tax competition in Finland is included.