INFORMATION-THEORETIC ASYMPTOTICS OF BAYES METHODS
INFORMATION-THEORETIC ASYMPTOTICS OF BAYES METHODS
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DOI：
10.1109/18.54897
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发表时间：
1990-05-01
影响因子：
2.5
通讯作者：
BARRON, AR
中科院分区：
文献类型：
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作者：
CLARKE, BS;BARRON, AR
在不知道真实密度函数的情况下，贝叶斯模型将n个随机变量序列的联合密度函数作为相对于先验的密度平均值。研究了真密度与贝叶斯密度之间的相对熵距离D/sub n/，并证明了其渐近距离为（d/2）（log n）+c，其中d为参数向量的维数.因此，相对熵速率D/sub n/n以速率（log n）/n收敛到零。常数c，作者明确指出，仅取决于先验密度函数和Fisher信息矩阵的真实参数值。密度估计，通用数据压缩，复合假设检验和股市投资组合选择的后果。<>
In the absence of knowledge of the true density function, Bayesian models take the joint density function for a sequence of n random variables to be an average of densities with respect to a prior. The authors examine the relative entropy distance D/sub n/ between the true density and the Bayesian density and show that the asymptotic distance is (d/2)(log n)+c, where d is the dimension of the parameter vector. Therefore, the relative entropy rate D/sub n//n converges to zero at rate (log n)/n. The constant c, which the authors explicitly identify, depends only on the prior density function and the Fisher information matrix evaluated at the true parameter value. Consequences are given for density estimation, universal data compression, composite hypothesis testing, and stock-market portfolio selection.<>