Matern52

class gpjax.kernels.Matern52(active_dims=None, lengthscale=1.0, variance=1.0, n_dims=None, compute_engine=<gpjax.kernels.computations.dense.DenseKernelComputation object>)

Bases: StationaryKernel

The Matérn kernel with smoothness parameter fixed at 2.5.

Computes the covariance for pairs of inputs \((x, y)\) with lengthscale parameter \(\ell\) and variance \(\sigma^2\).

\[ k(x, y) = \sigma^2 \Bigg(1 + \frac{\sqrt{5}\lvert x-y \rvert}{\ell} + \frac{5\lvert x - y \rvert^2}{3\ell^2}\Bigg)\exp\Bigg(-\frac{\sqrt{5}\lvert x-y\rvert}{\ell}\Bigg) \]

Parameters:

• active_dims (list[int] | slice)

• lengthscale (AbstractUnwrappable)

• variance (AbstractUnwrappable)

• n_dims (int | None)

• compute_engine (AbstractKernelComputation)

property spectral_density: MultivariateStudentT

a multivariate Student’s t with 5 degrees of freedom and scale \(\mathrm{diag}(\ell)^{-1}\).

Type:

The spectral measure of the Matérn-5/2 kernel