added rendered and corrected GP solutions in the correct format

GP_Solutions.qmd

@@ -1,10 +1,23 @@
 ---
-title: "GP_Solutions"
-format: html
-editor: visual
+title: "VectorByte Methods Training:  Introduction to Gaussian Processes for Time Dependent Data (Practical - solution)"
+author:
+  - name: Parul Patil 
+    affiliation: Virginia Tech and VectorByte
+citation: true
+date: 2024-07-24
+date-format: long
+format:
+  html:
+    toc: true
+    toc-location: left
+    html-math-method: katex
+    css: styles.css
+bibliography: references.bib
+link-citations: TRUE
 ---
 
-##### Libraries
+
+# Libraries
 
 ```{r, warning=FALSE, message=FALSE, warn.conflicts = FALSE}
 library(mvtnorm)
@@ -13,7 +26,7 @@ library(hetGP)
 library(ggplot2)
 ```
 
-##### HetGP (sin wave eg)
+# HetGP (sin wave eg)
 
 ```{r}
 # Your turn
@@ -50,7 +63,7 @@ nugs <- het_pred$nugs
 summary(nugs)
 ```
 
-##### Challenges
+# Challenges
 
 We need to load the data and the functions
 
@@ -86,7 +99,9 @@ fx.sin <- function(datetime, f1 = fx.iso_week){
 }
 ```
 
-###### Fit a GP Model for the location "SERC" i.e. `site_number = 7`.
+## Fit a GP Model for the location "SERC" 
+
+i.e. `site_number = 7`.
 
 Just change site = 7
 
@@ -191,7 +206,7 @@ rmse <- sqrt(mean((yt_true - yt_pred)^2))
 rmse
 ```
 
-###### Use an environmental predictor in your model. Following is a function `fx.green` that creates the variable given the `datetime` and the `location`.
+## Use an environmental predictor in your model. Following is a function `fx.green` that creates the variable given the `datetime` and the `location`.
 
 Here is a snippet of the supporting file that you will use; You can look into the data.frame and try to plot `ker` for one site at a time and see what it yields.
 
@@ -215,7 +230,7 @@ fx.green <- function(datetime, site, site_info = df_green){
 -   set up X3 using `fx_green`
 -   Scale X3
 
-Setting up the target dataframe
+### Setting up the target dataframe
 
 ```{r}
 
@@ -234,7 +249,7 @@ df_train <- subset(df, df$datetime <= cutoff)
 df_test <- subset(df, df$datetime > cutoff)
 ```
 
-Adding Greenness
+### Adding Greenness
 
 ```{r}
 # Choose location 
@@ -333,7 +348,7 @@ rmse <- sqrt(mean((yt_true - yt_pred)^2))
 rmse
 ```
 
-###### Fit a GP Model for all the locations (*More advanced*).
+## Fit a GP Model for all the locations (*More advanced*).
 
 ```{r}
 # GP function. This can be varied but easiest way is to just take in X, y, XX and return the predicted means and bounds. 

docs/Stats_review.html

@@ -353,7 +353,7 @@ <h1>Random Variables (RVs)</h1>
 <li>discrete (numbers of items or successes)</li>
 <li>continuous (heights, times, weights)</li>
 </ul>
-<p>We usually use capital letters – e.g.&nbsp;<span class="math inline">X</span>, <span class="math inline">Y</span>, sometimes with bold or with subscripts – to denote the RVs. In contrast we use lower case letters, e.g.&nbsp;<span class="math inline">x</span>, <span class="math inline">y</span>, <span class="math inline">k</span>, to denote the values that the RV takes. For instance, lets say that the heights of the woman at Virginia Tech are the RV, <span class="math inline">X</span>, and <span class="math inline">X</span> has a normal distribution with mean 62 inches and variance 6<span class="math inline">^2</span>, i.e., <span class="math inline">X \sim \mathrm{N}(62,6^2)</span> distribution. Say we then observe the heights of 3 individuals drawn from this distribution – we would write this as: <span class="math inline">x=(</span> 63.4, 56.8, 67.3 <span class="math inline">)</span>.</p>
+<p>We usually use capital letters – e.g.&nbsp;<span class="math inline">X</span>, <span class="math inline">Y</span>, sometimes with bold or with subscripts – to denote the RVs. In contrast we use lower case letters, e.g.&nbsp;<span class="math inline">x</span>, <span class="math inline">y</span>, <span class="math inline">k</span>, to denote the values that the RV takes. For instance, lets say that the heights of the woman at Virginia Tech are the RV, <span class="math inline">X</span>, and <span class="math inline">X</span> has a normal distribution with mean 62 inches and variance 6<span class="math inline">^2</span>, i.e., <span class="math inline">X \sim \mathrm{N}(62,6^2)</span> distribution. Say we then observe the heights of 3 individuals drawn from this distribution – we would write this as: <span class="math inline">x=(</span> 60.6, 58.6, 71.6 <span class="math inline">)</span>.</p>
 <p><br> <br> </p>
 </section>
 <section id="probability-distributions" class="level1">
@@ -577,7 +577,7 @@ <h1>Probability Distributions in <code>R</code></h1>
 <div class="cell">
 <div class="sourceCode cell-code" id="cb3"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb3-1"><a href="#cb3-1" aria-hidden="true" tabindex="-1"></a><span class="fu">rnorm</span>(<span class="dv">3</span>, <span class="at">mean=</span><span class="dv">0</span>, <span class="at">sd=</span><span class="dv">1</span>) <span class="do">## random draws</span></span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 <div class="cell-output cell-output-stdout">
-<pre><code>[1]  0.4409249  1.0655151 -1.5581929</code></pre>
+<pre><code>[1]  0.3620634  0.7783175 -0.3565513</code></pre>
 </div>
 </div>
 <div class="cell">