一种基于密度核估计的最大熵方法

摘要

For the measurement data with unknown probability distribution, it has been proved that the probability distribution determined by the maximum entropy method (MEM) is a reasonable distribution with the least assumption. But the result of MEM is not always consistent with the properties of a probability density, the resulting truncation and normalization of the result would reduce the accuracy of MEM. A new method based on the maximum entropy principle which combines with kernel density estimate of a probability density is proposed. The estimate given by the new method is totally consistent with the properties of a probability density. The validity and accuracy of the new method are illustrated through examples.%针对未知概率分布类型的测量数据,采用最大熵方法可以确定被测量含有最少人为主观假设的概率分布.但经典最大熵方法由于其密度函数的数学形式导致全局优化难度较大,计算结果难以满足概率密度函数基本性质,需要截断及归一才能使用.本文通过引入概率密度核估计方法,对最大熵方法进行了改进,简化了计算过程,并证明了改进后计算结果能够满足概率密度函数基本性质,最后通过算例说明了该方法的有效性.