= Gaussian semivariogram
{c}
For $\phi>0$ and nonnegative <variances>, $\gamma(h)=\tau^2\mathbf1_{\{h\ne0\}}+\sigma^2(1-e^{-\phi^2\|h\|^2})$ admits <covariance> $C(h)=\sigma^2e^{-\phi^2\|h\|^2}+\tau^2\mathbf1_{\{h=0\}}$. The <Gaussian kernel> is positive definite because it is the <Fourier transform> of the density of a <Gaussian distribution>. Adding independent <white noise> supplies the <nugget effect>. Its scale is $a=1/\phi$. For $\sigma^2>0$, its exact <range of a semivariogram> is infinite. If $\sigma^2=0$, it is a pure <nugget effect> with no nontrivial structured range.
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