ON THE RATIONALE OF MAXIMUM-ENTROPY METHODS
ON THE RATIONALE OF MAXIMUM-ENTROPY METHODS
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DOI：
10.1109/proc.1982.12425
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发表时间：
1982-01-01
影响因子：
20.6
通讯作者：
JAYNES, ET
中科院分区：
文献类型：
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作者：
JAYNES, ET
我们讨论了最大熵（MAXENT）和其他方法的频谱分析，如舒斯特，Blackman-Tukey，最大似然，贝叶斯和自回归（AR，阿尔马，或ARIMA）模型之间的关系，强调它们并不冲突，而是在不同的问题是适当的。我们的结论是：1）“正统”采样理论方法在我们有已知的噪声特性模型（采样分布）但没有关于被估计量的可感知先验信息的问题中是有用的。2)MAXENT在我们有关于多重性的先验信息但没有噪声的问题中是最优的。3)完整的贝叶斯解决方案包括这两种特殊情况，并且在我们既有先验信息又有噪声的问题中需要。4)AR模型在某种意义上是MAXENT的特例，但在另一种意义上，它们在所有离散时间序列的谱分析问题中无处不在。5)经验方法，如Blackman-Tukey，甚至不调用似然函数，在问题的初步探索阶段是有用的，在这个阶段，我们的知识足以允许直观判断如何组织计算（平滑，抽取，窗口，预白化，用零填充等）。但不足以建立一个定量模型，为我们自动和最佳地做适当的事情。
We discuss the relations between maximum-entropy (MAXENT) and other methods of spectral analysis such as the Schuster, Blackman-Tukey, maximum-likelihood, Bayesian, and Autoregressive (AR, ARMA, or ARIMA) models, emphasizing that they are not in conflict, but rather are appropriate in different problems. We conclude that: 1) "Orthodox" sampling theory methods are useful in problems where we have a known model (sampling distribution) for the properties of the noise, but no appreciable prior information about the quantities being estimated. 2) MAXENT is optimal in problems where we have prior information about multiplicities, but no noise. 3) The full Bayesian solution includes both of these as special cases and is needed in problems where we have both prior information and noise. 4) AR models are in one sense a special case of MAXENT, but in another sense they are ubiquitous in all spectral analysis problems with discrete time series. 5) Empirical methods such as Blackman-Tukey, which do not invoke even a likelihood function, are useful in the preliminary, exploratory phase of a problem where our knowledge is sufficient to permit intuitive judgments about how to organize a calculation (smoothing, decimation, windows, prewhitening, padding with zeroes, etc.) but insufficient to set up a quantitative model which would do the proper things for us automatically and optimally.