I work with heart rate variability signals and I'm trying to calculate the confidence interval of the PSD estimates using Python. So I looked at Richard Shiavi, Applied Statistical Signal Analysis book. I found that the Chi-square distribution can be used to determine the CI. The author gives the following relationship:
2*K*Ik(m)/L1
Hi Rhenan!
To obtain confidence interval (CI) i use another approach. For probability level alpha=0.9972 (look for 3sigma rule) I solve two equation for left and right boundary.
(1-alpha)/2=integral(PSD(x),-inf,x);
(1+alpha)/2=integral(PSD(x),-inf,x);
if you solve it, you will find left and right boundaries of CI.
Hi Oleksii Vodka, thank you very much! I'll implement a code to solve these equations.
But to use the 3sigma rule the PSD distribution must be normal?
No. I mean that alpha=0.9972 is probability under normal low with 3sigma rule. But you can define alpha in another way.
Rhenan, have you looked at the following article?
Torrence, C. & Compo, G. P. A practical guide to wavelet analysis Bulletin of the American Meteorological Society, American Meteorological Society, 1998, 79, 61-78
It's mostly about wavelet analysis and significance tests. Section 4 explains theoretical spectrum and significance levels for both wavelets and Fourier spectra. I have translated their code from Matlab to Python, included some improvements and also received contributions from other people around the globe who found a couple of mistakes. My code is available at https://github.com/regeirk/pycwt
The lines of code that calculate the significance of a given signal are in module wav.py (579--712).
Enjoy!
Hi Sebastian Krieger, thank you very much!
I just figured out last sunday how to find the inverse cdf of the chi squared using chi2.ppf([1 - alpha / 2, alpha / 2], 2 * dof), just like you did in your code.
By the way, great job with your wavelet module!
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