Hi Aki, I have a quick question about this paper. I am try to trying to implement the approximation for an exponential covariance function (\nu = 1/2), which isn’t explicitly presented in the paper
But, it should be pretty straightforward to substitute into the formula for Matern class spectral density. When I did this, however, I noticed that the 4\pi^2 factor seems to be missing from equations (1), (2), and (3). Looking at some of the reference materials I also noticed that Rasmussen and Williams use one convention of the Fourier transform with the 2\pi in the power of the complex exponential and Solin and Särkkä use a convention with a \frac{1}{2\pi} factor outside the integral.
I did a little testing and the method in the Riutort et al. methods works with the equations (1), (2), and (3) as presented but seemingly not if one re-derives them using the Rasmussen and Williams spectral density equation and keeps the 4\pi^2 factor.
Can you provide any clarity here?