Small‐sphere distributions for directional data with application to medical imaging

We propose novel parametric concentric multi‐unimodal small‐subsphere families of densities for p ? 1 ≥ 2‐dimensional spherical data. Their parameters describe a common axis for K small hypersubspheres, an array of K directional modes, one mode for each subsphere, and K pairs of concentrations parameters, each pair governing horizontal (within the subsphere) and vertical (orthogonal to the subsphere) concentrations. We introduce two kinds of distributions. In its one‐subsphere version, the first kind coincides with a special case of the Fisher–Bingham distribution, and the second kind is a novel adaption that models independent horizontal and vertical variations. In its multisubsphere version, the second kind allows for a correlation of horizontal variation over different subspheres. In medical imaging, the situation of p ? 1 = 2 occurs precisely in modeling the variation of a skeletally represented organ shape due to rotation, twisting, and bending. For both kinds, we provide new computationally feasible algorithms for simulation and estimation and propose several tests. To the best knowledge of the authors, our proposed models are the first to treat the variation of directional data along several concentric small hypersubspheres, concentrated near modes on each subsphere, let alone horizontal dependence. Using several simulations, we show that our methods are more powerful than a recent nonparametric method and ad hoc methods. Using data from medical imaging, we demonstrate the advantage of our method and infer on the dominating axis of rotation of the human knee joint at different walking phases.     

Mortality analysis of persons with disabilities in Argentina by age,sex and duration of benefit, 2015–16

This article describes the differential mortality of Argentina’s disability pension beneficiaries during the 2015–16 period, based on National Social Security Administration (Administración Nacional de la Seguridad Social – ANSES) payment records. It compares data for those with an assessed disability with overall population data, as well as with available international data (from Canada, Chile, Mexico, and the United States of America). In addition to breaking down mortality rates for people with disabilities by age and sex, it also factors in duration of benefit, establishing an inverse correlation between benefit duration and mortality.     

On the almost sure convergence for sums of negatively superadditive dependent random vectors in Hilbert spaces and its application

Abstract

This paper develops almost sure convergence for sums of negatively superadditive dependent random vectors in Hilbert spaces, we obtain Chung type SLLN and the Jaite type SLLN for sequences of negatively superadditive dependent random vectors in Hilbert spaces. Rate of convergence is studied through considering almost sure convergence to 0 of tail series. As an application, the almost sure convergence of degenerate von Mises-statistics is investigated.     

学派勃兴与学科崛起——李比希学派对吉森大学化学学科兴起的历史贡献及现实省思

19世纪20年代到50年代,德国吉森大学的化学学科实现了从寂寂无闻到跻身世界一流的历史转变,不但使吉森大学成为当时学界公认的“化学圣地”,同时还直接推动德国取代法国成为新的国际化学学术中心。在这一进程中,由著名化学家李比希依托吉森大学化学实验室创立的李比希学派发挥了至关重要的作用。作为近代史上第一个依托大学形成的科学学派,李比希学派在近代大学史上开辟了全新的基于实验室的化学教学科研模式,奠定了吉森大学在近代化学领域特别是有机化学和应用化学领域的领军地位,并且以高水平和多渠道的学术交流极大提升了吉森大学化学学科的学术地位和国际影响。以李比希学派为参照,中国大学在建设世界一流学科进程中,应着力培育学术核心人物并充分发挥其引领作用,积极探索符合学科个性需求的特色化学术生长点,同时努力打造一支具有高度内聚性的学术团队。     

Goodness-of-fit tests based on the distance between the Dirichlet process and its base measure

The Dirichlet process is a fundamental tool in studying Bayesian nonparametric inference. The Dirichlet process has several sum representations, where each one of these representations highlights some aspects of this important process. In this paper, we use the sum representations of the Dirichlet process to derive explicit expressions that are used to calculate Kolmogorov, Lévy, and Cramér–von Mises distances between the Dirichlet process and its base measure. The derived expressions of the distance are used to select a proper value for the concentration parameter of the Dirichlet process. These tools are also used in a goodness-of-fit test. Illustrative examples and simulation results are included.     

Testing independence based on Bernstein empirical copula and copula density

In this paper we provide three nonparametric tests of independence between continuous random variables based on the Bernstein copula distribution function and the Bernstein copula density function. The first test is constructed based on a Cramér-von Mises divergence-type functional based on the empirical Bernstein copula process. The two other tests are based on the Bernstein copula density and use Cramér-von Mises and Kullback–Leibler divergence-type functionals, respectively. Furthermore, we study the asymptotic null distribution of each of these test statistics. Finally, we consider a Monte Carlo experiment to investigate the performance of our tests. In particular we examine their size and power which we compare with those of the classical nonparametric tests that are based on the empirical distribution function.     

An integral formula for the distribution of self-normalized Gaussian random samples

Given i.i.d. Gaussian random variables and after standardizing the sample by subtracting the sample mean and dividing it by the sample deviation, we obtain an integral formula for the distribution of these self-normalized variables. Using geometrical arguments, we obtain the distribution of each and the joint distribution of two of them. These formulas can be used to calculate the expected value of the particular type of Cramér von Mises statistic to test normality.     

Error analysis of stochastic flight trajectory prediction models

This paper focuses on the analysis of errors between a flight trajectory prediction model and flight data. A novel stochastic prediction flight model is compared with the popular fly-by and fly-over turn models. The propagated error is measured using either spatial coordinates or angles. Depending on the case, the distribution of error is estimated and confidence bounds for the linear and directional mean are provided for all three stochastic flight models.