Densities with Gaussian Tails

Consider densities fi(t), for i = 1, ..., d, on the real line which have thin tails in the sense that, for each i, fi(t) ∼ γi(t)e−ψi(t), where γi behaves roughly like a constant and ψi is convex, C2, with ψ′ → ∞ and ψ″ > 0 and l/√ψ″ is self-neglecting. (The latter is an asymptotic variation condition.) Then the convolution is of the same form ft * ... *fd(t) ∼ γ(t)e − ψ(t) Formulae for γ, ψ are given in terms of the factor densities and involve the conjugate transform and infimal convolution of convexity theory. The derivations require embedding densities in exponential families and showing that the assumed form of the densities implies asymptotic normality of the exponential familie

Variability in disease phenotypes within a single PRNP genotype suggests the existence of multiple natural sheep scarpie strains within Europe

Variability of pathological phenotypes within classical sheep scrapie cases has been reported for some time, but in many instances it has been attributed to differences in the PRNP genotype of the host. To address this issue we have examined by immunohistochemistry (IHC) and Western blotting (WB) for the disease-associated form of the prion protein (PrPd), the brains of 23 sheep from five European countries, all of which were of the same ARQ/ARQ genotype. As a result of IHC examinations, sheep were distributed into five groups with different phenotypes and the groups were the same regardless of the scoring method used, ‘long’ or ‘short’ PrPd profiling. The groups made did not respond to the geographical origin of the cases and did not correlate with the vacuolar lesion profiles, which showed a high individual variability. Discriminatory IHC and WB methods coincided to detect a ‘CH1641-like’ case but otherwise correlated poorly in the classification of disease phenotypes. No other polymorphisms of the PRNP gene were found that could account for the pathological differences, except perhaps for a sheep from Spain with a mutation at codon 103 and a unique pathological phenotype. Preliminary evidence indicates that those different IHC phenotypes correlate with distinct biological properties on bioassay, suggesting that they are indicative of strain diversity. We therefore conclude that natural scrapie strains exist and that they can be revealed by detailed pathological examinations, which can be harmonized between laboratories to produce comparable results

Using Extreme Value Theory for Determining the Probability of Carrington-Like Solar Flares

Space weather events can negatively affect satellites, the electricity grid, satellite navigation systems and human health. As a consequence, extreme space weather has been added to the UK and other national risk registers. By their very nature, extreme space weather events occur rarely and, therefore, statistical methods are required to determine the probability of their occurrence. Space weather events can be characterised by a number of natural phenomena such as X-ray (solar) flares, solar energetic particle (SEP) fluxes, coronal mass ejections and various geophysical indices (Dst, Kp, F10.7). In this paper extreme value theory (EVT) is used to investigate the probability of extreme solar flares. Previous work has assumed that the distribution of solar flares follows a power law. However such an approach can lead to a poor estimation of the return times of such events due to uncertainties in the tails of the probability distribution function. Using EVT and GOES X-ray flux data it is shown that the expected 150-year return level is approximately an X60 flare whilst a Carrington-like flare is a one in a 100-year event. It is also shown that the EVT results are consistent with flare data from the Kepler space telescope mission.Comment: 13 pages, 4 figures; updated content following reviewer feedbac

On the modelling of the excesses of galaxy clusters over high-mass thresholds

In this work we present for the first time an application of the Pareto approach to the modelling of the excesses of galaxy clusters over high-mass thresholds. The distribution of those excesses can be described by the generalized Pareto distribution (GPD), which is closely related to the generalized extreme value (GEV) distribution. After introducing the formalism, we study the impact of different thresholds and redshift ranges on the distributions, as well as the influence of the survey area on the mean excess above a given mass threshold. We also show that both the GPD and the GEV approach lead to identical results for rare, thus high-mass and high-redshift, clusters. As an example, we apply the Pareto approach to ACT-CL J0102-4915 and SPT-CL J2106-5844 and derive the respective cumulative distribution functions of the exceedance over different mass thresholds. We also study the possibility to use the GPD as a cosmological probe. Since in the maximum likelihood estimation of the distribution parameters all the information from clusters above the mass threshold is used, the GPD might offer an interesting alternative to GEV-based methods that use only the maxima in patches. When comparing the accuracy with which the parameters can be estimated, it turns out that the patch-based modelling of maxima is superior to the Pareto approach. In an ideal case, the GEV approach is capable to estimate the location parameter with a percent level precision for less than 100 patches. This result makes the GEV based approach potentially also interesting for cluster surveys with a smaller area.Comment: 10 pages, 8 figures, MNRAS accepted, minor modifications to match the accepted versio

Compellingly high SARS-CoV-2 susceptibility of Golden Syrian hamsters suggests multiple zoonotic infections of pet hamsters during the COVID-19 pandemic

Golden Syrian hamsters (Mesocricetus auratus) are used as a research model for severe acute respiratory syndrome coronavirus type 2 (SARS-CoV-2). Millions of Golden Syrian hamsters are also kept as pets in close contact to humans. To determine the minimum infective dose (MID) for assessing the zoonotic transmission risk, and to define the optimal infection dose for experimental studies, we orotracheally inoculated hamsters with SARS-CoV-2 doses from 1 * 105 to 1 * 10-4 tissue culture infectious dose 50 (TCID50). Body weight and virus shedding were monitored daily. 1 * 10-3 TCID50 was defined as the MID, and this was still sufficient to induce virus shedding at levels up to 102.75 TCID50/ml, equaling the estimated MID for humans. Virological and histological data revealed 1 * 102 TCID50 as the optimal dose for experimental infections. This compelling high susceptibility leading to productive infections in Golden Syrian hamsters must be considered as a potential source of SARS-CoV-2 infection for humans that come into close contact with pet hamsters

Estimation of conditional laws given an extreme component

Let $(X,Y)$ be a bivariate random vector. The estimation of a probability of the form $P(Y\leq y \mid X >t)$ is challenging when $t$ is large, and a fruitful approach consists in studying, if it exists, the limiting conditional distribution of the random vector $(X,Y)$, suitably normalized, given that $X$ is large. There already exists a wide literature on bivariate models for which this limiting distribution exists. In this paper, a statistical analysis of this problem is done. Estimators of the limiting distribution (which is assumed to exist) and the normalizing functions are provided, as well as an estimator of the conditional quantile function when the conditioning event is extreme. Consistency of the estimators is proved and a functional central limit theorem for the estimator of the limiting distribution is obtained. The small sample behavior of the estimator of the conditional quantile function is illustrated through simulations.Comment: 32 pages, 5 figur

Clinical and Pathologic Features of H-Type Bovine Spongiform Encephalopathy Associated with E211K Prion Protein Polymorphism

The majority of bovine spongiform encephalopathy (BSE) cases have been ascribed to the classical form of the disease. H-type and L-type BSE cases have atypical molecular profiles compared to classical BSE and are thought to arise spontaneously. However, one case of H-type BSE was associated with a heritable E211K mutation in the prion protein gene. The purpose of this study was to describe transmission of this unique isolate of H-type BSE when inoculated into a calf of the same genotype by the intracranial route. Electroretinograms were used to demonstrate preclinical deficits in retinal function, and optical coherence tomography was used to demonstrate an antemortem decrease in retinal thickness. The calf rapidly progressed to clinical disease (9.4 months) and was necropsied. Widespread distribution of abnormal prion protein was demonstrated within neural tissues by western blot and immunohistochemistry. While this isolate is categorized as BSE-H due to a higher molecular mass of the unglycosylated PrPSc isoform, a strong labeling of all 3 PrPSc bands with monoclonal antibodies 6H4 and P4, and a second unglycosylated band at approximately 14 kDa when developed with antibodies that bind in the C-terminal region, it is unique from other described cases of BSE-H because of an additional band 23 kDa demonstrated on western blots of the cerebellum. This work demonstrates that this isolate is transmissible, has a BSE-H phenotype when transmitted to cattle with the K211 polymorphism, and has molecular features that distinguish it from other cases of BSE-H described in the literature

On Max-Stable Processes and the Functional D-Norm

We introduce a functional domain of attraction approach for stochastic processes, which is more general than the usual one based on weak convergence. The distribution function G of a continuous max-stable process on [0,1] is introduced and it is shown that G can be represented via a norm on functional space, called D-norm. This is in complete accordance with the multivariate case and leads to the definition of functional generalized Pareto distributions (GPD) W. These satisfy W=1+log(G) in their upper tails, again in complete accordance with the uni- or multivariate case. Applying this framework to copula processes we derive characterizations of the domain of attraction condition for copula processes in terms of tail equivalence with a functional GPD. \delta-neighborhoods of a functional GPD are introduced and it is shown that these are characterized by a polynomial rate of convergence of functional extremes, which is well-known in the multivariate case.Comment: 22 page

A regional Bayesian POT model for flood frequency analysis

Flood frequency analysis is usually based on the fitting of an extreme value distribution to the local streamflow series. However, when the local data series is short, frequency analysis results become unreliable. Regional frequency analysis is a convenient way to reduce the estimation uncertainty. In this work, we propose a regional Bayesian model for short record length sites. This model is less restrictive than the index flood model while preserving the formalism of "homogeneous regions". The performance of the proposed model is assessed on a set of gauging stations in France. The accuracy of quantile estimates as a function of the degree of homogeneity of the pooling group is also analysed. The results indicate that the regional Bayesian model outperforms the index flood model and local estimators. Furthermore, it seems that working with relatively large and homogeneous regions may lead to more accurate results than working with smaller and highly homogeneous regions