Bayesian sequential joint detection and estimation

Abstract

Joint detection and estimation refers to deciding between two or more hypotheses and, depending on the test outcome, simultaneously estimating the unknown parameters of the underlying distribution. This problem is investigated in a sequential framework under mild assumptions on the underlying random process. We formulate an unconstrained sequential decision problem, whose cost function is the weighted sum of the expected run-length and the detection/estimation errors. Then, a strong connection between the derivatives of the cost function with respect to the weights, which can be interpreted as Lagrange multipliers, and the detection/estimation errors of the underlying scheme is shown. This property is used to characterize the solution of a closely related sequential decision problem, whose objective function is the expected run-length under constraints on the average detection/estimation errors. We show that the solution of the constrained problem coincides with the solution of the unconstrained problem with suitably chosen weights. These weights are characterized as the solution of a linear program, which can be solved using efficient off-the-shelf solvers. The theoretical results are illustrated with two example problems, for which optimal sequential schemes are designed numerically and whose performance is validated via Monte Carlo simulations.     

Sequential testing for exponential and pareto distributions

This paper deals with the exact calculation of the decision boundaries for sequential probability ratio test for simple hypotheses and alternatives in the case of an exponential or a Pareto distribution. The calculations also enable one to give some idea of the mean sample size for the sequential test.     

变步长法计算标准正态分布函数与函数模块设计

对标准正态分布函数公式进行恒等变形,再用变步长法计算正态分布函数值,并用VB6．0完成该函数计算功能模块的程序设计。在大气预测模式程序设计过程中,该模块可被直接调用,有助于预测模式的连续、快速计算。     

Parameter Estimation Under Failure-Censored Constant-Stress Life Testing Model: A Bayesian Approach

Abstract

This article compares likelihood and Bayesian estimations for partially accelerated constant-stress life test model under type II censoring assuming Pareto distribution of the second kind. Both maximum likelihood and Bayesian estimators of the model parameters are derived. The posterior means and posterior variances are obtained under the squared error loss function using Lindley's approximation procedure. The advantages of this proposed procedure are shown. Monte Carlo simulations are conducted under different samples sizes and different parameter values to assess and compare the proposed methods of estimation. A noninformative prior on the model parameters is used to make the comparison more meaningful. It has been observed that Lindley's method usually provides posterior variances and mean squared errors smaller than those of the maximum likelihood estimators. That is, Lindley's method produces improved estimates, which is an advantage of this method.     

Discrete distribution of implanted and annealed arsenic atoms in silicon nanowires and its effect on device performance

We have theoretically investigated the effects of random discrete distribution of implanted and annealed arsenic (As) atoms on device characteristics of silicon nanowire (Si NW) transistors. Kinetic Monte Carlo simulation is used for generating realistic random distribution of active As atoms in Si NWs. The active As distributions obtained through the kinetic Monte Carlo simulation are introduced into the source and drain extensions of n-type gate-all-around NW transistors. The current–voltage characteristics are calculated using the non-equilibrium Green''s function method. The calculated results show significant fluctuation of the drain current. We examine the correlation between the drain current fluctuation and the factors related to random As distributions. We found that the fluctuation of the number of dopants in the source and drain extensions has little effect on the on-current fluctuation. We also found that the on-current fluctuation mainly originated from the randomness of interatomic distances of As atoms and hence is inherent in ultra-small NW transistors.     

基于风险的油田油气集输管线维护决策优化方法

将长输管道最优完整性维护决策方法——损失函数法应用于油气集输管线的维护决策优化.该方法以油田油气集输管线的风险检测和风险评价结果为基础,通过引入决策准则、后果函数、状态集及决策集等概念,并对油气集输管线失效后果量化,进而建立决策优化数学模型.通过计算各决策的损失函数确定最优的维护决策方案,应用此方法对某原油外输管线进行了维护决策优化,达到了较好的维护效果.     

An Asymptotic Second-Order Lower Bound for the Bayes Risk of a Sequential Procedure

Abstract

Consider the problem of estimating the difference of the means of two populations, where each population distribution is a member of the one-parameter exponential family of probability distributions. A Bayesian approach is adopted in which the mean difference is estimated under the squared error loss and the prior distributions are of the form proposed by Diaconis and Ylivisaker [Diaconis, P.; Ylivisaker, D. Conjugate priors for exponential families. Ann. of Statist. 1979, 6, 269–281]. The main result determines an asymptotic second-order lower bound for the Bayes risk of a sequential procedure that takes N observations from one population and t ? N from the other population, and estimates the mean difference by the Bayes estimator, where N is determined according to a sequential design and t denotes the total number of observations sampled from both populations.     

新型垂直筛板液体分散性能研究

液体分散性能是喷射型塔板重要的流体力学特性。文中在６００ｍｍ的有机玻璃塔上对新型垂直筛板的液体分散性能进行了研究。结果表明气相板孔动能因子、板上清液层高度和液体的物性是影响液体分散性能的重要因素,液滴粒度分布可以用上限对数正态分布函数来描述。     

Sequential and two-stage point estimation for the range in a power family distribution

Sequential and two-stage point estimation procedures for the range of a power family distribution are discussed using a loss function from a fairly general class.

Some asymptotic characteristics of the sequential procedure are presented, including approximate expressions for the distribution of the sample size. For the two stage procedure, we present asymptotic properties and exact expressions for the risk of the procedure, and distribution and mean of the stopping rule. The results of numerical simulations are presented to demonstrate some practical merits of our procedures for moderate sample sizes.     

Computational estimation of the triacylglycerol composition of vegetable fats from gas and liquid chromatography data

A mathematical framework was described and discussed that relates the triacylglycerol (TAG) distribution to measurements results. This model is valid for any analytical technique for which an unambiguous relation between the TAGs and the experimental data exists. The framework can be employed to estimate the TAG distribution based on any subset of these analytical techniques. Furthermore future techniques can be incorporated, eventually enabling the computation of the exact TAG distribution. In current practice the relation from measurement values to the TAG distribution is believed to be described by Coleman's theory. However some natural fats and fractions of fats are known to be non‐adherent to Coleman's theory. For both palm stearin and palm kernel oil this notion is tested and confirmed. For these fats a different approach is needed to be able to estimate the TAG distribution. Within the framework three different approaches for making an estimation of the TAG distribution based on measured data are described, discussed and compared with Coleman's results: a least squares approach, a genetic algorithm (GA) approach and an expectation maximisation (EM) approach. The results presented demonstrate that the estimated TAG distributions from the GA and EM algorithm are significantly better than Coleman's estimate and the least squares approach. Overall the EM algorithm is favoured because of its consistency.     

Poisson parameters of antimicrobial activity: a quantitative structure-activity approach

A contingency of observed antimicrobial activities measured for several compounds vs. a series of bacteria was analyzed. A factor analysis revealed the existence of a certain probability distribution function of the antimicrobial activity. A quantitative structure-activity relationship analysis for the overall antimicrobial ability was conducted using the population statistics associated with identified probability distribution function. The antimicrobial activity proved to follow the Poisson distribution if just one factor varies (such as chemical compound or bacteria). The Poisson parameter estimating antimicrobial effect, giving both mean and variance of the antimicrobial activity, was used to develop structure-activity models describing the effect of compounds on bacteria and fungi species. Two approaches were employed to obtain the models, and for every approach, a model was selected, further investigated and found to be statistically significant. The best predictive model for antimicrobial effect on bacteria and fungi species was identified using graphical representation of observed vs. calculated values as well as several predictive power parameters.     

The Use of Thin Film Thermocouples to Determine the Thermal Conductivity and Young's Modulus of Coatings and Interfaces

Linear and differential thin film thermocouples, typically 500-1000Å thick, were fabricated on flexible polymer and paper substrates by thermal evaporation. Both types of thermocouples had thermal sensitivities of approximately 4 μ V/°C, for temperatures between 20°C and 40°C, on the paper and polymer-coated paper substrates. The transverse thermal conductivity (k^t), i.e., thermal conductivity in the direction perpendicular to the plane of the films, of polyimide (Kapton-H®) films, of a clay-coated paper, and of a polystyrene coating on paper were determined by depositing linear thermocouples on both sides of the films and raising the temperature of one junction and measuring the heat flux and, at equilibrium, the temperature of the other junction. Shear and Young's moduli of the polymer films were estimated from the measured thermal conductivity values, assuming the Debye model of thermal conductivity.     

On sequentially adaptive asymptotically efficient rank statistics

For the simple regression model ( containing the two—sample location model as a special case ), adaptive ( linear ) rank statistics arising in the context of ( asymtotically) efficient testing and estimation procedures are considered. An orthonormal system based on the classical Legendre polynomial system is incorporated in the adaptive determination of the score generating function, and the proposed sequential procedure is based on a suitably posed stopping rule. Various properties of this sequentailly adaptive procedure and the allied stopping rule are studied. Asymptotic linearity results ( in a shift or regression parameter ) of linear rank statistics are studied with special reference to the Legendre polynomial system and some improved rates of convergence are estabilished in this context.     

Modifications of carbon for polymer composites and nanocomposites

The various forms of carbon used in composite preparation include mainly carbon-black, carbon nanotubes and nanofibers, graphite and fullerenes. This review presents a detailed literature survey on the various modifications of the carbon nanostructures for nanocomposite preparation focusing upon the works published in the last decade. The modifications of each form of carbon are considered, with a compilation of structure-property relationships of carbon-based polymer nanocomposites. Modifications in both bulk and surface modifications have been reviewed, with comparison of their mechanical, thermal, electrical and barrier properties. A synopsis of the applications of these advanced materials is presented, pointing out gaps to motivate potential research in this field.