A Look at Randomness in Microsoft Windows Solitaire,or, Using Electronic Games of Chance for Statistics Projects

The popular computer game Solitaire is used as a vehicle for investigating random number generation. This can form a very good basis for classroom projects.     

经典DSmT证据组合规则的随机集表示

由于信息的多样性和复杂性,使得对不确定信息的表示和建模都要通过相应的方法完成。由于方法的不统一,难以实现对异类不确定信息的融合。寻找一种统一的理论实现多源异类信息的表示与建模,已成为信息融合领域中的关键问题。已有研究成果表明,随机集理论有望解决该难题。介绍了一种新的不确定推理理论-DSm理论,引入了随机集理论的基本概念和性质,以随机集为工具,给出了经典DSm组合规则的随机集表示,从而将DSmT纳入基于随机集理论的不确定信息统一表示与建模架构中。     

“随机信号分析”课程中探究式教学的探索与实践

探究式教学能够促使学生理解并掌握所学知识,提高学生分析问题、解决问题的综合能力。本文探寻适合“随机信号分析”课程的探究式教学模式,并且进行实际应用和探讨。实践结果表明,该方法能充分发挥学生的主观能动性,收到了很好的教学效果。     

Variance reduction in large graph sampling

The norm of practice in estimating graph properties is to use uniform random node (RN) samples whenever possible. Many graphs are large and scale-free, inducing large degree variance and estimator variance. This paper shows that random edge (RE) sampling and the corresponding harmonic mean estimator for average degree can reduce the estimation variance significantly. First, we demonstrate that the degree variance, and consequently the variance of the RN estimator, can grow almost linearly with data size for typical scale-free graphs. Then we prove that the RE estimator has a variance bounded from above. Therefore, the variance ratio between RN and RE samplings can be very large for big data. The analytical result is supported by both simulation studies and 18 real networks. We observe that the variance reduction ratio can be more than a hundred for some real networks such as Twitter. Furthermore, we show that random walk (RW) sampling is always worse than RE sampling, and it can reduce the variance of RN method only when its performance is close to that of RE sampling.     

Some limsup results for increments of stable processes in random scenery

In this paper, we prove some limsup results for increments and lag increments ofG(t), which is a stable processe in random scenery. The proofs rely on the tail probability estimation ofG(t). Project (No. 10071072) supported by National Natural Science Foundation of China     

Firm-related training tracks: a random effects ordered probit model

A random effects ordered response model of training is estimated to analyze the existence of training tracks and time varying coefficients in training frequency. Two waves of a Dutch panel survey of workers are used covering the period 1992–1996. The amount of training received by workers increased during the period 1994–1996 compared to 1992–1994. Evidence is found for the existence of training tracks in the amount of training courses taken. It is further found that the effects of individual characteristics such as education, age and gender on training should be treated as individual varying coefficients.     

时滞随机线性系统的结构特点及其最优控制

针对离散时滞随机线性系统的结构特点,探讨了不同情况下的最优控制算法。当受控对象各控制通路中滞后时间间隔都相同,且输入为随机信号时,可采用二次函数型最优控制定律和分离定理。而对于滞后间隔不断变化的复杂系统,可采用滞后补偿器原理。在极限情况下,这些方法还可推广到连续系统。通过例子可以看到算法并不增加系统状态变量的维数。     

Some limsup results for increments of stable processes in random scenery

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