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The mean of x is subtracted before calculating the fft. However, the sample mean is ofcourse a biased estimate - especially if we have short chains. But we have a less biased estimate of the mean of a parameter if we use the mean from all chains+walkers. It should be slightly better for too short chains.
(An alternative idea is to calculate the ACF and the tau from the first-differences - Then there would be no need to center).
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