Estimating sample mean under interval uncertainty and constraint on sample variance

Traditionally, practitioners start a statistical analysis of a given sample x₁, … , x_n by computing the sample mean E and the sample variance V. The sample values x_i usually come from measurements. Measurements are never absolutely accurate and often, the only information that we have about the corresponding measurement errors are the upper bounds Δ_i on these errors. In such situations, after obtaining the measurement result , the only information that we have about the actual (unknown) value x_i of the ith quantity is that x_i belongs to the interval . Different values x_i from the corresponding intervals lead, in general, to different values of the sample mean and sample variance. It is therefore desirable to find the range of possible values of these characteristics when x_i ∈ x_i.Often, we know that the values x_i cannot differ too much from each other, i.e., we know the upper bound V₀ on the sample variance V : V ? V₀. It is therefore desirable to find the range of E under this constraint. This is the main problem that we solve in this paper.     

Effect of microstructure on the nucleation of deformation twins in polycrystalline high-purity magnesium: A multi-scale modeling study

A multi-scale, theoretical study of twin nucleation from grain boundaries in polycrystalline hexagonal close packed (hcp) metals is presented. A key element in the model is a probability theory for the nucleation of deformation twins based on the idea that twins originate from a statistical distribution of defects in the grain boundaries and are activated by local stresses at the grain boundaries. In this work, this theory is integrated into a crystal plasticity constitutive model in order to study the influence of these statistical effects on the microstructural evolution of the polycrystal, such as texture and twin volume fraction. Recently, a statistical analysis of exceptionally large data sets of {101?2} deformation twins was conducted for high-purity Mg (Beyerlein et al., 2010a). To demonstrate the significantly enhanced accuracy of the present model over those employing more conventional, deterministic approaches to twin activation, the model is applied to the case of {101?2} twinning in Mg to quantitatively interpret the many statistical features reported for these twins (e.g., variant selection, thickness, numbers per grain) and their relationship to crystallographic grain orientation, grain size, and grain boundary misorientation angle. Notably the model explains the weak relationship observed between crystal orientation and twin variant selection and the strong correlation found between grain size and the number of twins formed per grain. The predictions suggest that stress fluctuations generated at grain boundaries are responsible for experimentally observed dispersions in twin variant selection.     

基于统计量的差分吸收光谱烟气SO2浓度反算方法

提出了一种基于统计量的差分吸收光谱SO2浓度反算方法,利用差分吸收度标准差的大小表征SO2浓度的高低.使用主元素分析(principle component analysis,PCA)方法对差分吸收光谱进行处理,将处理结果、信号相关度与标准差结合为综合统计量,用于反算SO2的浓度.该方法应用于光程为0.3 m的烟气浓度...     

什么是统计

通俗介绍了统计的意义,对统计规律性等进行了探讨,指出大数据是统计学发展的新阶段.     

β-CYCLODEXTRIN REGULATED STEREOREGULARITY AND MOLECULAR WEIGHT IN INCLUSION POLYMERIZATION OF ACRYLONITRILE

Polyacrylonitrile (PAN) polymers were prepared by inclusion polymerization of the monomer using various molar equivalents of β-cyclodextrin (β-CD). Stereoregular (isotactic, atactic and syndiotactic) distributions of the prepared PAN polymers were determined from terminal model Bernoullian statistics using ¹³C-NMR data. With an increase in acrylonitrile (AN): β-CD ratios, the proportion of isotactic polymers increased. Also, T_g increased along with degradation temperature at higher AN: β-CD ratios. However, molecular weight of the polymers prepared was lower at an AN: β-CD ratio of 10:1, but was found to be larger than the control at an AN: β-CD ratio of 20:1.     

红外导数光谱-统计学法区别鉴定麦冬及其伪品的研究

为了建立中药材麦冬及其伪品的直接鉴定的理论和方法 ,采用OMNI采样器直接测定法测定了样品的红外光谱 ,并经过二阶导数光谱转换后进行峰位一致率检验。结果发现麦冬表皮以内部分和外表皮的二阶导数红外光谱峰位基本无差别 ,而且不同产地的道地药材具有较好的相关性。研究中发现浙麦冬与川麦冬表皮以内部分的二阶导数FTIR峰值 (χ2c =891 882 ,P =0 0 0 0 )的差异性极显著 ;与土麦冬 (χ2c=4 2 9 2 17,P =0 0 0 0 )、与湖北麦冬 (χ2c=6 92 70 6 ,P =0 0 0 0 )、与短葶山麦冬 (χ2c=981 970 ,P =0 0 0 0 )、与阔叶山麦冬 (χ2c=716 2 17,P =0 0 0 0 )、与竹叶麦冬 (χ2c=70 1 393,P =0 0 0 0 )的差异性都极显著。实验结果表明二阶导数红外光谱结合统计学法可用于中药材麦冬的真伪鉴别 ,本法简便、快速和准确     

Paretian Poisson Processes

Many random populations can be modeled as a countable set of points scattered randomly on the positive half-line. The points may represent magnitudes of earthquakes and tornados, masses of stars, market values of public companies, etc. In this article we explore a specific class of random such populations we coin ‘Paretian Poisson processes’. This class is elemental in statistical physics—connecting together, in a deep and fundamental way, diverse issues including: the Poisson distribution of the Law of Small Numbers; Paretian tail statistics; the Fréchet distribution of Extreme Value Theory; the one-sided Lévy distribution of the Central Limit Theorem; scale-invariance, renormalization and fractality; resilience to random perturbations.     

飞行器定位误差的统计分布

本文研究飞行器飞行过程中的定位误差,通过对试验数据的分析,利用统计理论结合软件探求了误差的分布,得到了比较满意的结果,这一研究对实际应用有着比较重要的意义。     

Geometry of sample spaces

In statistics, independent, identically distributed random samples do not carry a natural ordering, and their statistics are typically invariant with respect to permutations of their order. Thus, an n-sample in a space M can be considered as an element of the quotient space of $M^n$ modulo the permutation group. The present paper takes this definition of sample space and the related concept of orbit types as a starting point for developing a geometric perspective on statistics. We aim at deriving a general mathematical setting for studying the behavior of empirical and population means in spaces ranging from smooth Riemannian manifolds to general stratified spaces.We fully describe the orbifold and path-metric structure of the sample space when M is a manifold or path-metric space, respectively. These results are non-trivial even when M is Euclidean. We show that the infinite sample space exists in a Gromov–Hausdorff type sense and coincides with the Wasserstein space of probability distributions on M. We exhibit Fréchet means and k-means as metric projections onto 1-skeleta or k-skeleta in Wasserstein space, and we define a new and more general notion of polymeans. This geometric characterization via metric projections applies equally to sample and population means, and we use it to establish asymptotic properties of polymeans such as consistency and asymptotic normality.     

Bayesian size-and-shape regression modelling

Building on Dryden et al. (2021), this note presents the Bayesian estimation of a regression model for size-and-shape response variables with Gaussian landmarks. Our proposal fits into the framework of Bayesian latent variable models and, potentially, allows for a highly flexible modelling framework.