关于"条件概率"的几个问题

一、条件概率的意义 :条件概率是概率论中的一个很重要的概念。设 A,B是两个事件 ,且 P( A) >0 ,定义 P( B|A) =P( AB)P( A) ,并称之为在已知事件 A已经发生的条件下 ,事件 B发生的条件概率。条件概率的意义 ,可以从以下三个方面来阐述 :1 .几何直观意义我们可用单位正方形表示样本空间Ω。用正方形内任一封闭曲线围成的图形表示事件 ,而把图形的面积理解为相应事件的概率。设 A Ω ,B Ω ,(见图 1 )图 1无条件概率 (或称为绝对概率 ) P( B) =P( B)P(Ω ) (注意 P(Ω ) =1 ) ,几何直观上 ,相当于 B在空间Ω中所占的比例。亦可表…     

算子概率范数与共鸣定理

提出概率赋范线性空间上集合有界性的简化定义,利用算子概率范数概念。进一步研究概率赋范线性空间上的线性算子理论,并在算子概率赋范空间上,建立了概率有界、概率半有界、非概率无界意义下的共鸣定理。     

两个典型条件概率问题的错解浅析

1.条件概率:就是事件A在另外一个事件B已经发生的条件下的发生概率.条件概率表示为P(A|B),读作"在事件B发生的条件下事件A发生的概率".示例:根据大量的统计,大熊猫活到十岁的概率是0.8,活到十五岁的概率是0.6,若现有一只大熊猫已经十岁了,则他活到十五岁的概率是多少?需要注意的是,在上述定义中A与B之间不一     

区间概率信息条件下的风险型决策问题的解法探讨

区间概率信息条件下的决策问题是介于不确定型决策与风险型决策之间的一类特殊的决策问题。基于区间概率的定义及其数学特征,利用最大熵准则将区间概率转化为点概率,从而实现了区间概率信息条件决策问题的求解。     

二维随机变量条件分布函数教学的思考

本文利用条件概率的定义,由随机变量分布函数的性质,给出一般情形下随机变量条件分布函数的定义,以帮助学生更好地理解随机变量的条件分布函数的概念.     

基于模糊数的模糊事件概率的结构元表示

Zadeh[1]定义了在概率清晰和事件模糊条件下,模糊事件的概率表示.不过,用[1]表示概率,求解繁杂且困难.为此,利用结构元理论,定义了模糊数事件概率的表达式.不仅证明其与经典定义等价,且证明了模糊数事件复合表达形式.最后,给出了关于模糊数不等式的概率的表达式.通过算倒可看出,运用本方法求解模糊数事件概率比较简捷.     

简单随机抽样的一个注记

对简单随机抽样两种定义的关系进行了讨论,澄清了教科书中的一些模糊不清之处;通过反例举证了两种定义在某种意义下的不等价性;给出了变概率抽样与不等概率抽样的定义,指出变概率抽样与不等概率抽样也可以是简单随机抽样;本文最后,给出了简单随机抽样的更具一般性的(广义)定义.     

关于概率算子测度的弱收敛

概率算子测度（ＰＯＭ）是量子检测与估值的理论基础．本文研究了ＰＯＭ的弱收问题，还讨论了Ｈｉｌｂｅｒｔ空间上不同拓扑意义下的ＰＯＭ弱收敛的相互关系．     

条件概率真度的相似度及伪距离

基于条件概率的思想,在连续值命题逻辑系统中引入赋值密度函数概念,给出了公式的概率真度、条件概率真度的定义,定义了公式间的相似度和伪距离并证明了概率真度的推理规则.     

全概率公式的推广

首先给出了普通事件在普通条件和Fuzzy条件下的Fuzzy条件概率及Fuzzy事件在普通条件和Fuzzy条件下的Fuzzy条件概率公式,并通过对普通事件的全概率公式进行推广,得到普通事件和Fuzzy事件分别在普通划分和Fuzzy划分下的全概率公式     

A NEW CHARACTERIZATION OF THE BINOMIAL SEQUENCE

ＡＮＥＷＣＨＡＲＡＣＴＥＲＩＺＡＴＩＯＮＯＦＴＨＥＢＩＮＯＭＩＡＬＳＥＱＵＥＮＣＥ￥ＣＨＥＮＧＳＨＩＸＵＥＡｂｓｔｒａｃｔ：Ｉｎｔｈｉｓｐａｐｅｒ，ａｎｅｗｃｈａｒａｃｔｅｒｉｚａｔｉｏｎｏｆｔｈｅｂｉｎｏｍｉａｌｓｅｑｕｅｎｃｅａｎｄｉｔｓｅｑｕｉ...     

Application of auxiliary Markov chains to start-up demonstration tests

We use auxiliary Markov chains to derive probabilistic results for five types of start-up demonstration tests, with start-ups that are Markovian of a general order. Four of the tests are based on consecutive (or total) successful start-ups and consecutive (or total) failures; the fifth has two rejection criteria. For each test type, we obtain the probability of the test ending with acceptance of the unit, the probability distribution and moments of the number of start-ups in the test, the probability of acceptance (or rejection) of the equipment in a specified number of trials, and the conditional distribution of the number of start-ups in the test given that the unit is accepted or rejected. Numerical examples are given. Though the results are for these specific types of start-up demonstration tests, the method of derivation may be used for tests with other stopping criteria, and in other situations as well.     

Conditional Probability on the Kopka＇s D-posets

K?pka’s D-poset is a very important notion in quantum structures. In this paper the conditional probability on the K?pka’s D-posets is studied. The notion of conditional probability is introduced and the basic properties of conditional probability are proved.     

基于统计自然语言处理的央行货币政策研究

运用自然语言处理方法来分析货币政策,对数据采用绝对概率和条件概率方法分别分析.得出如下结论:第一,在我国近十几年的货币政策实施过程中,央行对于"通货膨胀"的关注度明显高于"通货紧缩".第二,通过统计有关通胀类词的出现个数,可以大致了解每年通货膨胀严重程度.第三,通过计算条件概率,可以更好的解释该给条件词十几年的大致走势.第四,通过不同时期的比较分析,在绝对概率下可以更好的看出用词的变迁,而在条件概率下,可以更好的研究给定词在不同时期所表现出来的不同特征.     

一类推广的带干扰风险模型的条件破产概率

本文首先利用随机时刻变换推广了一类带干扰的风险模型,然后讨论这类风险模型的条件破产概率.研究表明条件破产概率相对于无条件破产概率能提供更多有用信息,这对保险公司及时调整投资和管理策略是很有帮助的.     

Natural gradient algorithm for stochastic distribution systems with output feedback

In this paper, we use natural gradient algorithm to control the shape of the conditional output probability density function for the stochastic distribution systems from the viewpoint of information geometry. The considered system here is of multi-input and single output with an output feedback and a stochastic noise. Based on the assumption that the probability density function of the stochastic noise is known, we obtain the conditional output probability density function whose shape is only determined by the control input vector under the condition that the output feedback is known at any sample time. The set of all the conditional output probability density functions forms a statistical manifold (M), and the control input vector and the output feedback are considered as the coordinate system. The Kullback divergence acts as the distance between the conditional output probability density function and the target probability density function. Thus, an iterative formula for the control input vector is proposed in the sense of information geometry. Meanwhile, we consider the convergence of the presented algorithm. At last, an illustrative example is utilized to demonstrate the effectiveness of the algorithm.     

The Goodman–Nguyen relation within imprecise probability theory

The Goodman–Nguyen relation is a partial order generalising the implication (inclusion) relation to conditional events. As such, with precise probabilities it both induces an agreeing probability ordering and is a key tool in a certain common extension problem. Most previous work involving this relation is concerned with either conditional event algebras or precise probabilities. We investigate here its role within imprecise probability theory, first in the framework of conditional events and then proposing a generalisation of the Goodman–Nguyen relation to conditional gambles. It turns out that this relation induces an agreeing ordering on coherent or C-convex conditional imprecise previsions. In a standard inferential problem with conditional events, it lets us determine the natural extension, as well as an upper extension. With conditional gambles, it is useful in deriving a number of inferential inequalities.     

Existence of sufficient regular conditional probabilities

If a-field is sufficient for a family of probability measures defined on a-field then there exist regular determinations of the conditional probability of P, given, which are independent of the special measure, provided that is-regular. A counterexample shows that the-regularity of cannot be replaced by the assumption that each is approximable by a fixed compact system. In particular if a-field is sufficient for a family of probability measures defined on a separable-field and if each admits a regular conditional probability, given, a common regular conditional probability, given, need not exist.     

条件期望的两种定义及其等价性探讨

讨论随机变最在给定子σ代数下条件期望的定义,利用投影定理这一数学工具给出条件期望的几何定义,并通过对它与现今各种概率论基础或随机过程教材中常见的公理化定义相互等价性的证明,揭示了条件期望这一概念的内涵.