尹章才, 刘清全, 孙华涛. 全概率公式在时间地理中的应用研究[J]. 武汉大学学报 ( 信息科学版), 2013, 38(8): 954-957.
引用本文: 尹章才, 刘清全, 孙华涛. 全概率公式在时间地理中的应用研究[J]. 武汉大学学报 ( 信息科学版), 2013, 38(8): 954-957.
YIN Zhangcai, LIU Qingquan, SUN Huatao. Probability Model of Directed Movements Based on Total Probability Theorem[J]. Geomatics and Information Science of Wuhan University, 2013, 38(8): 954-957.
Citation: YIN Zhangcai, LIU Qingquan, SUN Huatao. Probability Model of Directed Movements Based on Total Probability Theorem[J]. Geomatics and Information Science of Wuhan University, 2013, 38(8): 954-957.

全概率公式在时间地理中的应用研究

Probability Model of Directed Movements Based on Total Probability Theorem

  • 摘要: 在已知起止点时间和位置及最大速度的条件下,针对移动对象的时空不确定性,利用全概率公式构建了定向移动的概率模型。首先,根据起止点时间和位置计算平均速度(即能到达目的地的最小速度),并在最小与最大速度之间随机离散出若干速度点,同时假设随机速度变量服从麦克斯韦-玻尔兹曼分布。然后,对任一速度值计算移动对象的可达范围及其几何概型,即在该速度取值条件下移动对象的条件概率。最后,在速度概率与基于速度条件的几何概率基础上,利用全概率原理能计算定向移动的时空概率分布。实验结果表明,随最大速度的增大,该概率的方差具有收敛性和稳定性,不同于已有概率模型的方差的分散性。

     

    Abstract: When the locations of an agent at two times,and its maximum velocity are known,the agent’s location between both those time instances is uncertain.We present a practical method,the total probability theorem,to approximate that uncertainty.First,the minimum(average) velocity from starting point to destination can be computed,and then many discrete speed values between the minimum and maximum velocity can be chosen randomly.The random speed variable V follows the Maxwell-Boltzmann distribution that describes particle speeds,and thus the probability density function of V,p(V),becomes applicable.Second,for a discrete speed value v,we calculate the agent’s reachable range(x,y) at any time t in time geography.The range follows a uniform distribution,and so at t we may obtain p(x,y | v,t),which is the conditional probability of(x,y) given the value of the random variable V,V=v.Finally,according to the total probability theorem,the probability distribution of the agent at time t,p(x,y|t),is obtained by the equation ∑p(V=v)·p(x,y | v,t) where the parameter V takes all values.When increasing the maximum velocity,experiments show that the total probability’ variance has a good convergence and steadiness,an improvement over the existing method’ divergence.

     

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