Questions tagged [covariance-function]

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Different regression models in clusters, same variance structure [closed]

I have data that can be clustered so that each cluster has its own set of both observations and variables. I want to fit a linear model on each cluster, but i want the clusters to share the same ...
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Spectral Density of a Stationary, Isotropic Gaussian Kernel

I intend to perform a simulation of a Gaussian process. To that end, I use a stationary, isotropic Gaussian covariance function (aka Gaussian kernel, or squared exponential kernel), $k(r)= \exp (-\...
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Deriving spectral measure

While reading this book, I got stuck on page 266 where the authors found the spectral measure $F(du)$ of the generalized covariance function $K(h) = \Gamma(-\alpha/2) |h|^{\alpha}, ~0<\alpha<2.$ ...
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Confirming the formula for the Spectral Density of a Matern Covariance Function

The Matérn Class of functions is given by $$k_M(r)=\frac{2^{1-\nu}}{\Gamma(\nu)}\left(\frac{r\sqrt{2\nu}}{l}\right)^{\nu} K_{\nu}\left(\frac{r\sqrt{2\nu}}{l}\right)$$ where $r=\Vert x-x'\Vert$. The ...