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| Titel |
Bayesian modeling and significant features exploration in wavelet power spectra |
| VerfasserIn |
D. V. Divine, F. Godtliebsen |
| Medientyp |
Artikel
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| Sprache |
Englisch
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| ISSN |
1023-5809
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| Digitales Dokument |
URL |
| Erschienen |
In: Nonlinear Processes in Geophysics ; 14, no. 1 ; Nr. 14, no. 1 (2007-02-12), S.79-88 |
| Datensatznummer |
250012129
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| Publikation (Nr.) |
 copernicus.org/npg-14-79-2007.pdf |
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| Zusammenfassung |
| This study proposes and justifies a Bayesian approach to modeling wavelet
coefficients and finding statistically significant features in wavelet power
spectra. The approach utilizes ideas elaborated in scale-space smoothing
methods and wavelet data analysis. We treat each scale of the discrete
wavelet decomposition as a sequence of independent random variables and then
apply Bayes' rule for constructing the posterior distribution of the smoothed
wavelet coefficients. Samples drawn from the posterior are subsequently used
for finding the estimate of the true wavelet spectrum at each scale. The
method offers two different significance testing procedures for wavelet
spectra. A traditional approach assesses the statistical significance against
a red noise background. The second procedure tests for homoscedasticity of
the wavelet power assessing whether the spectrum derivative significantly
differs from zero at each particular point of the spectrum. Case studies with
simulated data and climatic time-series prove the method to be a potentially
useful tool in data analysis. |
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