Chris Harrison writes:
I have just come across your paper in the 2009 American Scientist. Another problem that I frequently come across is when people do power spectral analyses of signals. If one has 1200 points (fairly modest in this day and age) then there are 600 power spectral estimates. People will then determine the 95% confidence limits and pick out any spectral estimate that sticks up above this, claiming that it is significant. But there will be on average 30 estimates that stick up too high or too low. So in general there will be 15 spectral estimates which are higher than the 95% confidence limit which could happen just by chance. I suppose that this means that you have to set a much higher confidence limit, which would depend on the number of data in your signal.
I would also like your opinion about a paper in the Proceedings of the National Academy of Science, “The causality analysis of climate change and large-scale
human crisis” by David D. Zhang, Harry F. Lee, Cong Wang, Baosheng Li, Qing Pei, Jane Zhang, and Yulun An.
These authors take whole series of annual data from 1500 to 1800, giving 301 data in all and do linear correlations between pairs of data sets them. But some of the data sets only have data at longer intervals, such as 25 years. So the authors linearly interpolate the data to give an annual signal and then assume that they still have 301 data. Is this legitimate?
1. For your spectral estimation problem, I think it would best to fit some sort of hierarchical model for the 600 parameters.
2. I didn’t actually read the paper, but from your description I’d think it might be a good idea for them to bootstrap their data to get standard errors.