Periodic kernel

The periodic kernel is an important prior when we’re trying to model periodic functions with the gaussian process:

\begin{equation}
 K(x, x') = \sigma^{2}  \, \exp\left(-\frac{2}{l^{2}} \sin^{2}\left(\pi \frac{|x-x'|}{p}\right)\right)
\end{equation}

Where ${\sigma }^2$ is the amplitude, $l$ the lengthscale and $p$ the period.