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Update docs/examples/oceanmodelling.py
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Signed-off-by: Daniel Dodd <daniel_dodd@icloud.com>
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daniel-dodd authored Sep 7, 2023
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Expand Up @@ -414,7 +414,7 @@ def plot_fields(
#
# This is reminiscent of a 3 dimensional [Helmholtz decomposition](https://en.wikipedia.org/wiki/Helmholtz_decomposition).
#
# The 2 dimensional decomposition motivates a different approach: placing priors on $\Psi$ and $\Phi$, allowing us to make assumptions directly about fundamental properties of $\mathbf{F}$. If we choose independent GP priors such that $\Phi \sim \mathcal{G P}\left(0, k_{\Phi}\right)$ and $\Psi \sim \mathcal{G P}\left(0, k_{\Psi}\right)$, then $\mathbf{F} \sim \mathcal{G P} \left(0, k_\text{Helm}\right)$ (since acting linear operations on a GPs give GPs).
# The 2-dimensional decomposition motivates a different approach: placing priors on $\Psi$ and $\Phi$, allowing us to make assumptions directly about fundamental properties of $\mathbf{F}$. If we choose independent GP priors such that $\Phi \sim \mathcal{G P}\left(0, k_{\Phi}\right)$ and $\Psi \sim \mathcal{G P}\left(0, k_{\Psi}\right)$, then $\mathbf{F} \sim \mathcal{G P} \left(0, k_\text{Helm}\right)$ (since acting linear operations on a GPs give GPs).
#
# For $\mathbf{X}, \mathbf{X}^{\prime} \in \mathbb{R}^2 \times \left\{0,1\right\}$ and $z, z^\prime \in \{0,1\}$,
#
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