Monte Carlo Based Ensemble Forecasting

Ensemble forecasting involves the use of several integrations of a numerical model. Even if this model is assumed to be known, ensembles are needed due to uncertainty in initial conditions. The ideas discussed in this paper incorporate aspects of both analytic model approximations and Monte Carlo arguments to gain some efficiency in the generation and use of ensembles. Efficiency is gained through the use of importance sampling Monte Carlo. Once ensemble members are generated, suggestions for their use, involving both approximation and statistical notions such as kernel density estimation and mixture modeling are discussed. Fully deterministic procedures derived from the Monte Carlo analysis are also described. Examples using the three-dimensional Lorenz system are described.     

关于有限2—拟质元群

文章推广了文献[3]、[14]的工作，研究元的阶至多含二个合数的有限群（称之为2-拟质元群），并给出了它们的完全分类，得到了一般结果，若G是2-拟质元群，则|π(G）|≤5，且当|π（G）|=5时，有：G为单群，用S（G）表示群G的可解根基，πe″（G）表示πe(G）中的合数集合，{πi,j=1,2，…,t}表示G的各连通图分支，π1表示含2的连通分支。     

核磁共振成像装置磁场的数值模拟

采取了二维有限元法模拟核磁共振成像（ＭＲＩ）装置的主磁场。给出了永磁材料的等效面电流层的数学物理模型，并对永磁材料的退磁化曲线进行了等效处理。然后，求出核磁共振成像装置的主磁场的能量泛函表达式，并给出了整个空间的磁力线分布，计算结果与实验相吻合，从而验证了这种方法的正确性。最后，提出了用被动补偿的方法来扩大均匀场区域。     

任意旋成面叶栅B类气动杂交命题周角函数型变分有限元解

本文建立了任意旋成面叶栅B型周角函数变分有限元方法,并成功地应用于轴流叶栅和离心叶栅的气动设计计算,从而可使叶型设计建立在更加科学和合理的基础之上。     

Asymptotics for the Finite Time Ruin Probability in the Renewal Model with Consistent Variation

Abstract

This paper investigates the finite time ruin probability in the renewal risk model. Under some mild assumptions on the tail probabilities of the claim size and of the inter-occurrence time, a simple asymptotic relation is established as the initial surplus increases. In particular, this asymptotic relation is requested to hold uniformly for the horizon varying in a relevant infinite interval. The uniformity allows us to consider that the horizon flexibly varies as a function of the initial surplus, or to change the horizon into any nonnegative random variable as long as it is independent of the risk system.     

Finite mixtures of natural exponential families

Let μ be a positive measure concentrated on R⁺ generating a natural exponential family (NEF) F with quadratic variance function V_F(m), m being the mean parameter of F. It is shown that v(dx) = (γ+x)μ(γ ≥ 0) (γ ≥ 0) generates a NEF G whose variance function is of the form l(m)Δ+cΔ(m), where l(m) is an affine function of m, Δ(m) is a polynomial in m (the mean of G) of degree 2, and c is a constant. The family G turns out to be a finite mixture of F and its length-biased family. We also examine the cases when F has cubic variance function and show that for suitable choices of γ the family G has variance function of the form P(m) + Q(m)m where P, Q are polynomials in m of degree m2 while Δ is an affine function of m. Finally we extend the idea to two dimensions by considering a bivariate Poisson and bivariate gamma mixture distribution.     

A note on non-negative mean square error estimation of regression estimators in randomized response surveys

Generalized regression estimators are considered for the survey population total of a quantitative sensitive variable based on randomized responses. Formulae are presented for ‘non-negative’ estimators of approximate mean square errors of these biased estimators when population and sample sizes are large.     

Biogeographical Analysis of Chemical Co‐Occurrence Data to Identify Priorities for Mixtures Research

A challenge with multiple chemical risk assessment is the need to consider the joint behavior of chemicals in mixtures. To address this need, pharmacologists and toxicologists have developed methods over the years to evaluate and test chemical interaction. In practice, however, testing of chemical interaction more often comprises ad hoc binary combinations and rarely examines higher order combinations. One explanation for this practice is the belief that there are simply too many possible combinations of chemicals to consider. Indeed, under stochastic conditions the possible number of chemical combinations scales geometrically as the pool of chemicals increases. However, the occurrence of chemicals in the environment is determined by factors, economic in part, which favor some chemicals over others. We investigate methods from the field of biogeography, originally developed to study avian species co‐occurrence patterns, and adapt these approaches to examine chemical co‐occurrence. These methods were applied to a national survey of pesticide residues in 168 child care centers from across the country. Our findings show that pesticide co‐occurrence in the child care center was not random but highly structured, leading to the co‐occurrence of specific pesticide combinations. Thus, ecological studies of species co‐occurrence parallel the issue of chemical co‐occurrence at specific locations. Both are driven by processes that introduce structure in the pattern of co‐occurrence. We conclude that the biogeographical tools used to determine when this structure occurs in ecological studies are relevant to evaluations of pesticide mixtures for exposure and risk assessment.     

On Covariances from Overlapping Samples

Three plans are proposed for repetitive sampling of the same finite population over time, and their efficiencies are evaluated.     

Determination of Sample Size for Distribution-free Tolerance Limits

Formulas for the moments of the better known probability distribution functions are available in the literature on the subject. Persons wishing to derive these formulas, however, may find standard methods to be quite laborious. For discrete probability functions, surprisingly compact and elegant derivations may be obtained by using finite difference operators. Examples of this approach are presented.