This function estimates the log power spectral density against the log frequency, and calculates a slope \(\alpha\).
calc_PSD(chain, max_freq = 0.1, filter_freq = TRUE, plot = FALSE)Returns a list with log frequencies, log PSDs, and slope and intercept estimates.
Matrix of n x d dimensions, n = iterations, d = dimensions sequence
The maximum frequency to be considered in PSD if filter_freq = TRUE. See also Details.
Boolean. Whether PSD only considers the frequencies between 0 and max_freq. The default setting is TRUE. See also Details.
Boolean. Whether to return a plot or the elements used to make it.
A number of studies have reported that cognitive activities contain a long-range slowly decaying autocorrelation. In the frequency domain, this is expressed as \(S(f)\) ~ \(1/f^{-\alpha}\), with \(f\) being frequency, \(S(f)\) being spectral power, and \(\alpha\) \(\epsilon\) \([0.5,1.5]\) is considered \(1/f\) scaling. See See zhu2018MentalSamplingMultimodal;textualsamplr for a comparison of Levy Flight and PSD measures for different samplers in multimodal representations.
The default frequency range in PSD analysis extends from 0 to 0.1, which is specified by max_freq. It is because the logarithmic spectral power density tends to flatten beyond a frequency of 0.1. As a result, some researchers (e.g., gildenNoiseHuman1995;nobracketssamplr; zhu2022UnderstandingStructureCognitive;nobracketssamplr) estimate the value of \(\alpha\) using only frequencies below 0.1. When filter_freq is set to FALSE, the frequency range will be from 0 to the Nyquist frequency.
set.seed(1)
chain1 <- sampler_mh(1, "norm", c(0,1), diag(1))
calc_PSD(chain1[[1]], plot= TRUE)
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