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[Docs] Typo in documentation of MaternKernel #2569

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DelonShen opened this issue Aug 22, 2024 · 0 comments
Open

[Docs] Typo in documentation of MaternKernel #2569

DelonShen opened this issue Aug 22, 2024 · 0 comments

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@DelonShen
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In the documentation for MaternKernel it's written that
$$k_{\rm Matern}(\mathbf x_1, \mathbf x_2) = \frac{2^{1-\nu}}{\Gamma(\nu)}(\sqrt{ 2\nu } d)^\nu K_\nu(\sqrt{ 2\nu } d) $$
where
$$d = (\mathbf x_1 - \mathbf x_2)^T \Theta^{-2} (\mathbf x_1 - \mathbf x_2).$$

Is this a typo? From comparing to Eq. (4.14) of Rasmussen and Williams (2006), my understanding is that it should be
$$d^{\color{red}2} = (\mathbf x_1 - \mathbf x_2)^T \Theta^{-2} (\mathbf x_1 - \mathbf x_2)$$
or equivalently
$$d = |\mathbf x_1 - \mathbf x_2| \times \Theta^{-1}$$

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