Hybrid Processing of Stochastic and Subjective Uncertainty Data

Uncertainty analyses typically recognize separate stochastic and subjective sources of uncertainty, but do not systematically combine the two, although a large amount of data used in analyses is partly stochastic and partly subjective. We have developed methodology for mathematically combining stochastic and subjective sources of data uncertainty, based on new "hybrid number" approaches. The methodology can be utilized in conjunction with various traditional techniques, such as PRA (probabilistic risk assessment) and risk analysis decision support. Hybrid numbers have been previously examined as a potential method to represent combinations of stochastic and subjective information, but mathematical processing has been impeded by the requirements inherent in the structure of the numbers, e.g., there was no known way to multiply hybrids. In this paper, we will demonstrate methods for calculating with hybrid numbers that avoid the difficulties. By formulating a hybrid number as a probability distribution that is only fuzzily known, or alternatively as a random distribution of fuzzy numbers, methods are demonstrated for the full suite of arithmetic operations, permitting complex mathematical calculations. It will be shown how information about relative subjectivity (the ratio of subjective to stochastic knowledge about a particular datum) can be incorporated. Techniques are also developed for conveying uncertainty information visually, so that the stochastic and subjective components of the uncertainty, as well as the ratio of knowledge about the two, are readily apparent. The techniques demonstrated have the capability to process uncertainty information for independent, uncorrelated data, and for some types of dependent and correlated data. Example applications are suggested, illustrative problems are shown, and graphical results are given.     

DEA评价模型应用的几点探讨

为更好地应用ＤＥＡ评价模型，本文讨论了ＤＥＡ模型中定性指标的模糊处理及权重分布的随机处理，运用主成分分析法对ＤＥＡ模型指标体系进行处理，并对ＤＥＡ评价结果进行了排队分析．     

Bayesian Estimation of Survival Functions under Stochastic Precedence

When estimating the distributions of two random variables, X and Y, investigators often have prior information that Y tends to be bigger than X. To formalize this prior belief, one could potentially assume stochastic ordering between X and Y, which implies Pr(X < or = z) > or = Pr(Y < or = z) for all z in the domain of X and Y. Stochastic ordering is quite restrictive, though, and this article focuses instead on Bayesian estimation of the distribution functions of X and Y under the weaker stochastic precedence constraint, Pr(X < or = Y) > or = 0.5. We consider the case where both X and Y are categorical variables with common support and develop a Gibbs sampling algorithm for posterior computation. The method is then generalized to the case where X and Y are survival times. The proposed approach is illustrated using data on survival after tumor removal for patients with malignant melanoma.     

Growth and Heat Resistance Kinetic Variation Among Various Isolates of Salmonella and its Application to Risk Assessment

The abilities of cells of a particular type of bacteria to leave lag phase and begin the process of dividing or surviving heat treatment can depend on the serotypes or strains of the bacteria. This article reports an investigation of serotype-specific differences in growth and heat resistance kinetics of clinical and food isolates of Salmonella. Growth kinetics at 19 degrees C and 37 degrees C were examined in brain heart infusion broth and heat resistance kinetics for 60 degrees C were examined in beef gravy using a submerged coil heating apparatus. Estimates of the parameters of the growth curves suggests a small between-serotype variance of the growth kinetics. However, for inactivation, the results suggest a significant between-serotype effect on the asymptotic D-values, with an estimated between-serotype CV of about 20%. In microbial risk assessment, predictive microbiology is used to estimate growth and inactivation of pathogens. Often the data used for estimating the growth or inactivation kinetics are based on measurements on a cocktail--a mixture of approximately equal proportions of several serotypes or strains of the pathogen being studied. The expected growth or inactivation rates derived from data using cocktails are biased, reflecting the characteristics of the fastest growing or most heat resistant serotype of the cocktail. In this article, an adjustment to decrease this possible bias in a risk assessment is offered. The article also presents discussion of the effect on estimating growth when stochastic assumptions are incorporated in the model. In particular, equations describing the variation of relative growth are derived, accounting for the stochastic variations of the division of cells. For small numbers of cells, the expected value of the relative growth is not an appropriate "representative" value for actual relative growths that might occur.     

柔而趋刚 刚柔相济——从言语奢化禁则看语用法制化趋势

语言制度有"约定"的正式语言制度与"俗成"的非正式语言制度之分,作为正式的语言制度,近年我国颁布的相关法规对言语奢化的语用异化行为提出了一系列具体禁则.这些禁则反映出语言制度创新"柔而趋刚"的语用法制化趋势,也体现出语用法制化"刚柔相济"的特征语用法规既具有人文亲和的柔性,又具有执法必严,违法必究的刚性张力.     

交通信息条件下道路和停车选择SUE模型及算法

考虑交通信息系统(advanced traveler information system,ATIS)对出行者道路和停车选择行为的影响,并将出行者分成两类:一类出行者使用ATIS,另一类不使用ATIS.在此基础上,构造了一个基于概率的随机用户均衡模型来描述ATIS条件下的道路和停车选择问题,并给出了相应的求解算法.最后,通过一个算例分析了模型及算法的使用效果.     

Further results for parallel systems with two heterogeneous exponential components

In this paper, we investigate ordering properties of lifetimes of parallel systems with two independent heterogeneous exponential components with respect to likelihood ratio and hazard rate orders. Two sufficient conditions are provided for likelihood ratio and hazard rate orders to hold between the lifetimes of two parallel systems, respectively. Moreover, we extend the results from exponential case to the proportional hazard rate models. The results established here strength some of the results known in the literature. Finally, some numerical examples are given to illustrate the theoretical results derived here as well.     

Recursive location and scale estimators

It is shown that a recursive estimator with the same asymptotic properties as the median has convergence properties in finite samples which depend heavily on the scale of the data. A simple modification which adjusts for the scale is suggested and its application illustrated on simulated data. The modified estimator has much improved properties which are similar to those of the sample (non-recursive) median.     

Some results on generalized ageing classes

In this paper we provide new results about generalized ageing classes on the excess lifetime of a renewal process. We also obtain some characterizations of generalized ageing classes by means of the residual life at random time.     

Non‐parametric Threshold Estimation for Models with Stochastic Diffusion Coefficient and Jumps

Abstract. We consider a stochastic process driven by diffusions and jumps. Given a discrete record of observations, we devise a technique for identifying the times when jumps larger than a suitably defined threshold occurred. This allows us to determine a consistent non‐parametric estimator of the integrated volatility when the infinite activity jump component is Lévy. Jump size estimation and central limit results are proved in the case of finite activity jumps. Some simulations illustrate the applicability of the methodology in finite samples and its superiority on the multipower variations especially when it is not possible to use high frequency data.