pymc.gp.cov.Periodic.power_spectral_density_approx

Periodic.power_spectral_density_approx(J)

Power spectral density approximation.

Technically, this is not a spectral density but these are the first m coefficients of the low rank approximation for the periodic kernel, which are used in the same way. J is a vector of np.arange(m).

The coefficients of the HSGP approximation for the Periodic kernel are given by:

\[\begin{split}\tilde{q}_j^2 = \frac{2 \text{I}_j (\\ell^{-2})}{\\exp(\\ell^{-2})} \\ \tilde{q}_0^2 = \frac{\text{I}_0 (\\ell^{-2})}{\\exp(\\ell^{-2})}\end{split}\]

where $text{I}_j$ is the modified Bessel function of the first kind.