Dirichlet先验下置换熵的有效贝叶斯估计
Efficient Bayesian estimation of permutation entropy with Dirichlet priors
摘要：
对于有序模式抽样服从独立多项分布的系统，提出了用贝叶斯统计方法估计排列熵的方法。它表明，PE后验分布是密切接近的标准Beta分布，其超参数可以直接估计从矩分析计算从观察到的有序模式计数。与以前使用frequentist方法得出的表达式的等价性也被证明。由于贝叶斯估计PE自然结合了不确定性和先验信息，传统的要求，$N \gg D!$有效地规避，允许PE估计，即使是非常短的时间序列。对一个具有光反馈的半导体激光器（SLWOF）系统的PE后验分布进行了自相似性检验，结果表明该系统的PE随时间呈周期性变化。
英文摘要：
Estimation of permutation entropy (PE) using Bayesian statistical methods is presented for systems where the ordinal pattern sampling follows an independent, multinomial distribution. It is demonstrated that the PE posterior distribution is closely approximated by a standard Beta distribution, whose hyperparameters can be estimated directly from moments computed analytically from observed ordinal pattern counts. Equivalence with expressions derived previously using frequentist methods is also demonstrated. Because Bayesian estimation of PE naturally incorporates uncertainty and prior information, the orthodox requirement that $N \gg D!$ is effectively circumvented, allowing PE to be estimated even for very short time series. Self-similarity tests on PE posterior distributions computed for a semiconductor laser with optical feedback (SLWOF) system show its PE to vary periodically over time.
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