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AdrianKriger authored Sep 7, 2023
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Expand Up @@ -8,6 +8,11 @@ description: "Spatial Statistics with R."
# (Geo)spatial Statistics with R (Meuse)
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<figure><center>
<img src="{{site.baseurl | prepend: site.url}}/img/preds.png" style="width: 800px; height: 300px; border: 0px">
<figcaption>Fig.1 - Inverse Distance Weighting, 2nd-order Ordinary Least Squares and Ordinary Kriging interpolation </figcaption>
</center></figure>

In this exercise, we will explore the concepts and applications of Deterministic and Stochastic Interpolation Methods. We traverse such technics as:

<!-- <iframe src="{{site.baseurl | prepend: site.url}}/img/plotly.html" style="width: 800px; height: 300px; border: 0px"></iframe> -->
Expand All @@ -17,17 +22,8 @@ In this exercise, we will explore the concepts and applications of Deterministic
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;b. Linear Regression
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;c. Inverse Distance Weighting
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;d. Ordinary Least Squares

<!-- <img src="/img/preds.png" alt="predictions" img> -->

&nbsp;&nbsp;&nbsp;**2) Stochastic methods**
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;a. Variograms and Kriging

<figure><center>
<img src="{{site.baseurl | prepend: site.url}}/img/preds.png" style="width: 800px; height: 300px; border: 0px">
<figcaption>Fig.1 - Inverse Distance Weighting, 2nd-order Ordinary Least Squares and Ordinary Kriging interpolation </figcaption>
</center></figure>

&nbsp;&nbsp;&nbsp;**3)** we also briefly highlight ways we can **interrogate the quality** of an interpolation with;
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;a. $N$-fold cross validation; and
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;b. Residual Mean Squared Error (rmse).
Expand All @@ -36,6 +32,6 @@ In this exercise, we will explore the concepts and applications of Deterministic
<img src="{{site.baseurl | prepend: site.url}}/img/5-fold.png" style="width: 800px; height: 300px; border: 0px">
<!-- <figcaption>Fig.2 - Inverse Distance Weighting, 2nd-order Ordinary Least Squares and Ordinary Kriging interpolation </figcaption> -->
</center></figure>

_____
For this assignment we use a dataset that is well-suited to illustrate these concepts. The [meuse](https://search.r-project.org/CRAN/refmans/sp/html/meuse.html) dataset which comes with the `gstat` package.
**meuse**: gives locations (on a regular grid) and topsoil heavy metal concentrations, along with a number of soil and landscape variables at the observation locations, collected in a flood plain of the river Meuse, near the village of Stein (NL). Heavy metal concentrations are from composite samples of an area of approximately 15 m x 15 m.

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