【摘要】 文章在信息熵的理论基础上,给出了求解最大熵问题的一般表述。应用最大熵原理,在信息缺失的条件下可以最大效率地实现对全局进行判断和决策。以打靶运动中运动员不同环数的分布概率为例,将最大熵问题归结为数学模型中常见的优化类线性规划问题,利用Lingo软件求解。首先分析了高分环数对运动员提高成绩的限制。然后给出了不同平均环数下最大熵值的变化,探究了不同最大熵值下概率的均匀性与对称性规律。从简单的模型出发得出最大熵值越大表明概率分布越均匀,以及熵值可以体现系统概率分布上的一致性的结论。更多还原

【Abstract】 By the theory of information entropy,this paper gives general statements of maximum entropy problem.With maximum entropy principle,it is possible to make global judgments and decisions in the absence of major information.Taken the example of probability distribution of divergent rings in shooting sports,the linear programming(LP)is solved based on Lingo,and the limitation of the high-score rings in this sport has been discussed.After showing the variety of maximum entropy in divergent mean value of rings,the data reveal the uniformity and symmetry of probability under different maximum entropy.From this simple model,we can conclude that entropy can demonstrate the consistency of probability distributions,and large entropy generally corresponds to high uniformity in probability.更多还原