Rapid surrogate testing of wavelet coherences
Rapid surrogate testing of wavelet coherences
复制标题
小波相干性的快速替代测试
DOI：
10.1051/epjnbp/2017000
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发表时间：
2017
期刊：
影响因子：
--
通讯作者：
Reuman, Daniel C.
中科院分区：
文献类型：
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作者：
Sheppard, Lawrence W.;Reid, Philip C.;Reuman, Daniel C.
背景小波相干方法的使用使得能够识别在复杂系统中发现的波动的相位之间的频率依赖关系，例如医学和其他生物时间序列。这些关系可能会照亮的因果机制，相关的变量调查。然而，需要计算密集的统计测试，以确保表观相位关系在统计上是显着的，同时考虑到虚假相位关系的趋势，以体现在短的数据延伸。利用该方法，我们对与变量之间不存在实际相位关系的零假设相关联的相干值的分布进行采样。该分布的性质取决于数据的互谱。通过描述的依赖性，我们展示了如何大量的值，从这个分布可以迅速生成，而不需要生成相应的许多小波transforms.ResultsAs示范的技术，我们适用于有效的测试方法，一个复杂的生物系统组成的人口时间序列的浮游生物在食物网，和某些环境的驱动程序。大量的频率依赖的相位关系，发现这些变量之间，我们的算法有效地确定每个产生的概率下的零假设，给定的长度和属性的data.ConclusionProper会计如何产生的偏见和小波相干值的交叉频谱特性提供了一个更好的理解下的零假设的预期结果。我们的新技术可以大大加快小波相干性的显著性测试。
BackgroundThe use of wavelet coherence methods enables the identification of frequency-dependent relationships between the phases of the fluctuations found in complex systems such as medical and other biological timeseries. These relationships may illuminate the causal mechanisms that relate the variables under investigation. However, computationally intensive statistical testing is required to ensure that apparent phase relationships are statistically significant, taking into account the tendency for spurious phase relationships to manifest in short stretches of data.MethodsIn this study we revisit Fourier transform based methods for generating surrogate data, with which we sample the distribution of coherence values associated with the null hypothesis that no actual phase relationship between the variables exists. The properties of this distribution depend on the cross-spectrum of the data. By describing the dependency, we demonstrate how large numbers of values from this distribution can be rapidly generated without the need to generate correspondingly many wavelet transforms.ResultsAs a demonstration of the technique, we apply the efficient testing methodology to a complex biological system consisting of population timeseries for planktonic organisms in a food web, and certain environmental drivers. A large number of frequency dependent phase relationships are found between these variables, and our algorithm efficiently determines the probability of each arising under the null hypothesis, given the length and properties of the data.ConclusionProper accounting of how bias and wavelet coherence values arise from cross spectral properties provides a better understanding of the expected results under the null hypothesis. Our new technique enables enormously faster significance testing of wavelet coherence.