概率结构与概率度量空间探讨

本文提出了概率结构空间的概念,引出了概率拓扑空间,S型概率度量空间,S型概率赋范空间,S型概率内积空间的概念,重点研究了S型概率度量空间及S型概率赋范空间的基本构造与它们同概率度量空间及概率赋范空间的关系。     

经典概率与量子概率

概率的置信度（主观）解释，确认度（逻辑）解释，频率（真实度）解释共享的帕斯卡公理，共享帕斯卡公理的概率我们统称其为经典概率，而概率概念在量子力学应用中带来的变化形成的概率称为量子概率，量子概率与经典概率在概念上有联系也有区别，借助于概率的“可视度解释”，将概率定义合理地引到单个事件及波的干涉，可将量子力 率解释与量子力学曲率解释联系起来，排除经验主义的纠缠，合理地解释电子的双缝干涉实验。     

关于概率向量与概率矩阵的性质

讨论了概率向量和概率矩阵的性质 ,得到了概率向量和概率矩阵的几个结果     

传统的概率计算方法融入全概率公式的研究

全概率公式是概率计算方法中非常有用的计算工具,为了使学生深刻体会它在概率论教学中的重要用途,填补全概率公式应用的不足,同时,也为了使传统的概率计算在方法及思路上有所创新,本文通过几个具体实例介绍了传统的概率计算方法中融入全概率公式的教学研究,并给出了详细讲解。阐述了在某些概率计算的教学中,教师不仅应该会用相应的传统概率计算方法,而且还应会使用全概率公式,以使概率论的教学方法不断改进,教学质量不断提高。     

关于概率向量与概率矩阵的性质

讨论了概率向量和概率矩阵的性质，得到了概率向量和概率矩阵的几个结果。     

广义概率空间

给出广义概率空间的定义及性质定理,在此基础上研究广义概率空间中广义条件概率、乘法定理和事件的相互独立性。并且用实例讨论广义概率的应用。     

概率空间与集值概率空间的关系

本文研究了概率空间与集值概率空间的关系,指出概率空间与集值概率空间可以相互诱导。证明集合是闭集,得到了K_x的结构表示定理,然后讨论了集值概率测度P_x_p和概率测度P_x的有关性质。     

初中概率题为什么颇有争议——兼谈可能性和概率教学

初中的概率是建立在等可能性基础上的古典概率,又是统计学中概率的理想结果．由于概率知识涉及到公平性,抛掷结果的偶然性及概率问题的不确定性等因素,较易受错误直觉的误导．虽然教材通过大量重复的实验,先获得频率稳定值,再概括概率定义,让学生经历实验、观察、猜想、验证活动,获得古典概率的计算方法．但学生在处理概率问题的计算时还是容易出错．概率问题为什么颇有争议,     

用概率树图法求解事件发生的概率

求事件发生的概率时，首先按事件先后发生的顺序画出概率树图，在概率树图上注明各个事件发生的概率，然后沿事件的终点重返始点，再利用概率的乘法公式和概率的可加性，即可求得事件发生的概率．     

全概率与逆概率公式及其应用

全概率公式和逆概率公式作为概率论中最为重要的两个公式,不论是在理论上还是在实践上都有着极为广泛的应用.本文着重介绍了全概率公式与逆概率公式的概念、特点以及它们的应用举例.     

仅发送者知道通道信息的可控概率隐形传态

采用推广测量法,在仅发送者Alice知道部分纠缠GHZ态通道信息的条件下,提出了实现可控概率隐形传态的方案。     

Neural decoding based on probabilistic neural network

Brain-machine interface (BMI) has been developed due to its possibility to cure severe body paralysis. This technology has been used to realize the direct control of prosthetic devices,such as robot arms,computer cursors,and paralyzed muscles. A variety of neural decoding algorithms have been designed to explore relationships between neural activities and movements of the limbs. In this paper,two novel neural decoding methods based on probabilistic neural network (PNN) in rats were introduced,the PNN decode...     

Predicting the shrinkage of thermal insulation mortar by probabilistic neural networks

This study explored the potential of using probabilistic neural networks （PNN） to predict shrinkage of thermal insulation mortar.Probabilistic results were obtained from the PNN model with the aid of Parzen non-parametric estimator of the probability density functions （PDF）.Five variables,water-cementitious materials ratio,content of cement,fly ash,aggregate and plasticizer,were employed for input variables,while a category of 56-d shrinkage of mortar was used for the output variable.A total of 192 groups of experimental data from 64 mixtures designed using JMP7.0 software were collected,of which 120 groups of data were used for training the model and the other 72 groups of data for testing.The simulation results showed that the PNN model with an optimal smoothing parameter determined by the curves of the mean square error （MSE） and the number of unrecognized probability densities （UPDs） exhibited a promising capability of predicting shrinkage of mortar.     

关于一种概率内积空间定义中错误的修正

本文以概率测度空间为背景,给出了合理的概率内积空间定义,并修正了一种现有定义中的一个错误.     

The Illusion of Linearity: Expanding the evidence towards probabilistic reasoning

Previous research has shown that – due to the extensive attention spent to proportional reasoning in mathematics education – many students have a strong tendency to apply linear or proportional models anywhere, even in situations where they are not applicable. This phenomenon is sometimes referred to as the ‘illusion of linearity’. For example, in geometry it is known that many students believe that if the sides of a figure are doubled, the area is doubled too. In this article, the empirical evidence for this phenomenon is expanded to the domain of probabilistic reasoning. First, we elaborate on the notion of chance and provide some reasons for expecting the over generalization of linear models in the domain of probability too. Afterwards, a number of well-known and less-known probabilistic misconceptions are described and analysed, showing that they have one remarkable characteristic in common: they can be interpreted in terms oft he improper application of linear relations. Finally, we report on an empirical investigation aimed at identifying the ability of 10^th and12^th grade students to compare the probabilities of two binomial chance situations. It appears that before instruction in probability, students have a good capability of comparing two events qualitatively, but at the same time they incorrectly quantify this qualitative insight as if the variables in the problem were linked by a linear relationship. Remarkably, these errors persist after instruction in probability. The potential of this study for improving the teaching and learning of probability, as well as suggestions for further research, are discussed. This revised version was published online in July 2006 with corrections to the Cover Date.     

概率布尔网络的动态行为研究

概率布尔网络是布尔网络的拓展。布尔网络和概率布尔网络已经广泛应用于生物系统模拟中。运用马尔科夫链模拟概率布尔网络的动态行为及采用消除趋势波动分析（DFA）方法,分析概率布尔网络的长程相关性特性发现,概率布尔网络的动态行为具有长程相关性,大部分概率布尔网络能呈现1/f波动,且产生1/f波动的噪声值和范围比布尔网络的大。     

Probabilistic analysis of linear elastic cracked structures

This paper presents a probabilistic methodology for linear fracture mechanics analysis of cracked structures. The main focus is on probabilistic aspect related to the nature of crack in material. The methodology involves finite element analysis; sta- tistical models for uncertainty in material properties, crack size, fracture toughness and loads; and standard reliability methods for evaluating probabilistic characteristics of linear elastic fracture parameter. The uncertainty in the crack size can have a significant effect on the probability of failure, particularly when the crack size has a large coefficient of variation. Numerical example is presented to show that probabilistic methodology based on Monte Carlo simulation provides accurate estimates of failure prob- ability for use in linear elastic fracture mechanics.     

Educational applications of probabilistic conjoint measurement models

This chapter is a survey of four different applications of probabilistic models to problems in educational measurement. The first, by Esdaille, is an analysis of the Bermuda Educational Assessment Programme's Primary 5 Mathematics Component. The second, by Shaw, presents a detailed comparison of two South African tests, one multiple choice and the other short response direct questions, and suggests that the medium correlation coefficient usually obtained in comparisons between scores obtained from multiple-choice items and direct questions can in part be attributed to design errors in some multiple choice items. The third study tests the assertions of some linguists and literary critics that it may not be possible to expect or derive normative understandings of irony. Smith's analysis of over 250 U.S. students' interpretations of ironic poetry shows otherwise. Finally, Valgeirsdóttir describes how a probabilistic model informed the iterative construction of a pencil and paper adaptive aptitude test in Iceland.     

Tracking multiple people under occlusion and across cameras using probabilistic models

Tracking multiple people under occlusion and across cameras is a challenging question for discussion. Furthermore, the cameras in this study are used to extend the field of view, which are distinguished from the same field of view. Such corre-spondence between multiple cameras is a burgeoning research subject in the area of computer vision. This paper effectively solves the problems of tracking multiple people who pass from one camera to another and segmenting people under occlusion using probabilistic models. The probabilistic models are composed ofblob model, motion model and color model, which make the most of the space, motion and color information. First, we present a color model that uses maximum likelihood estimation based on non-parametric kernel density estimation. Second, we introduce a blob model based on mean shift, which segments the body into many regions according to the color of each person in order to spatially localize the color features corresponding to the way people are dressed. Clothes can be any mixture of colors. Third, we bring forward a motion model based on statistical probability which indicates the movement position of the same person between two successive frames in a single camera. Finally, we effectively unify the three models into a general probabilistic model and attain a maximization likelihood probability image, which is used to segment the foreground region under occlusion and to match people across multiple cameras.