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Fixed small mistake in FRK_intro.Rnw (missing escape characters)
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andrewzm committed Dec 26, 2023
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2 changes: 1 addition & 1 deletion vignettes/FRK_intro.Rnw
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Expand Up @@ -313,7 +313,7 @@ GridBAUs1 <- auto_BAUs(manifold = plane(), # 2D plane
nonconvex_hull=FALSE) # convex hull
@

\noindent The \tt{auto\_BAUs} function takes several arguments (see \tt{help(auto\_BAUs)} for details). Above, we instruct the helper function to construct BAUs on the plane, centred around the data \tt{meuse} with each BAU of size 100 $\times$ 100 (with units in m since the data is supplied with x-y coordinates in m). The \tt{type="grid"} input instructs that we want a rectangular grid and not a hexagonal lattice (use \tt{"hex"} for a hexagonal lattice), and \tt{convex=-0.05} is a specific parameter controlling the buffer-width of the spatial-domain boundary. The name `convex' was chosen as it is also used to control the buffer in case a non-convex hull is desired by setting \tt{nonconvex\_hull=TRUE} (see \tt{fmesher::fm_nonconvex_hull_inla} for more details and note that {\bf fmesher} needs to be installed for this option to be set). For the $i$th BAU, we also need to attribute the element $\varv_i$ that describes the hetereoscedascity of the fine-scale variation for that BAU. As described in Section \ref{sec:SREModel}, this component encompasses all process variation that occurs at the BAU scale and only needs to be known up to a constant of proportionality, $\sigma^2_\xi$ or $\sigma^2_\delta$ (depending on the chosen model); this constant is estimated using maximum likelihood with \tt{SRE.fit} using the EM algorithm of Section \ref{sec:estimation}. Typically, geographic features such as altitude are appropriate, but in this case we will just set this parameter to unity. It is important that this field is labelled `fs':
\noindent The \tt{auto\_BAUs} function takes several arguments (see \tt{help(auto\_BAUs)} for details). Above, we instruct the helper function to construct BAUs on the plane, centred around the data \tt{meuse} with each BAU of size 100 $\times$ 100 (with units in m since the data is supplied with x-y coordinates in m). The \tt{type="grid"} input instructs that we want a rectangular grid and not a hexagonal lattice (use \tt{"hex"} for a hexagonal lattice), and \tt{convex=-0.05} is a specific parameter controlling the buffer-width of the spatial-domain boundary. The name `convex' was chosen as it is also used to control the buffer in case a non-convex hull is desired by setting \tt{nonconvex\_hull=TRUE} (see \tt{fmesher::fm\_nonconvex\_hull\_inla} for more details and note that {\bf fmesher} needs to be installed for this option to be set). For the $i$th BAU, we also need to attribute the element $\varv_i$ that describes the hetereoscedascity of the fine-scale variation for that BAU. As described in Section \ref{sec:SREModel}, this component encompasses all process variation that occurs at the BAU scale and only needs to be known up to a constant of proportionality, $\sigma^2_\xi$ or $\sigma^2_\delta$ (depending on the chosen model); this constant is estimated using maximum likelihood with \tt{SRE.fit} using the EM algorithm of Section \ref{sec:estimation}. Typically, geographic features such as altitude are appropriate, but in this case we will just set this parameter to unity. It is important that this field is labelled `fs':

<<>>=
GridBAUs1$fs <- 1 # fine-scale variation at BAU level
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