small changes and fixes

GP.qmd

@@ -212,6 +212,7 @@ Y_n \\
 \end{aligned}
 \end{equation}
 ```
+
 ## Hyper Parameters
 
 . . .
@@ -222,11 +223,9 @@ One of the most common kernels which we will focus on is the squared exponential
 
 $$C_n = \exp{ \left( -\frac{\vert\vert x - x' \vert \vert ^2}{\theta} \right ) + g \mathbb{I_n}} $$
 
-. . .
-
-Recall, $$\Sigma_n = \tau^2 C_n$$
-
-We have three main parameters here:
+. . . 
+
+Recall, $\Sigma_n = \tau^2 C_n$. We have three main parameters here:
 
 -   $\tau^2$: Scale
 
@@ -417,7 +416,7 @@ Here, $\theta$ = ($\theta_1$, $\theta_2$, ..., $\theta_m$) is a vector of length
 
 . . .
 
--   Heteroskedasticity implies that the data is noisy, and thee noise is irregular.
+-   Heteroskedasticity implies that the data is noisy, and the noise is irregular.
 
 ```{r hetviz, echo = FALSE, cache=F, warning=FALSE, message=FALSE, dev.args = list(bg = 'transparent'), fig.width= 6, fig.height= 4, fig.align="center", warn.conflicts = FALSE}
 

GP_Notes.qmd

@@ -120,7 +120,7 @@ $\Sigma_{X_1 \vert X_2} = \Sigma_{11} - \Sigma_{12}\Sigma_{22}^{-1} \Sigma_{21}$
 
 Now, let's look at this in our context.
 
-Suppose we have, $D_n = (X_n, Y_n)$ where $Y_n \sim N \ ( \ 0 \ , \ \Sigma_n \ )$. Now, for a new location $x_p$, we need to find the distribution of$Y(x_p)$.
+Suppose we have, $D_n = (X_n, Y_n)$ where $Y_n \sim N \ ( \ 0 \ , \ \Sigma_n \ )$. Now, for a new location $x_p$, we need to find the distribution of $Y(x_p)$.
 
 We want to find the distribution of $Y(x_p) \ \vert \ D_n$. Using the information from above, we know this is normally distributed and we need to identify then mean and variance. Thus, we have
 

GP_Practical.qmd

@@ -170,11 +170,10 @@ head(target)
 \begin{equation}
 \begin{aligned}
 f(y) \ & = \text{log } \ (y + 1) \ \ ; \ \ \ \\[2pt]
-<!-- \ & = \sqrt{y} \ \ \ \; \ \ \ otherwise -->
 \end{aligned}
 \end{equation}
 
-We pass in ($response$ + 1) into this function to ensure we don';t take a log of 0. We will adjust this in our back transform. 
+We pass in (`response` + 1) into this function to ensure we don't take a log of 0. We will adjust this in our back transform. 
 
 Let's write a function for this, as well as the inverse of the transform.
 
@@ -380,7 +379,7 @@ Now, we will create a grid from the first week in our dataset to 1 year into the
 startdate <- as.Date(min(df$datetime))# identify start week
 grid_datetime <- seq.Date(startdate, Sys.Date() + 365, by = 7) # create sequence from 
 
-# Build the inpu space for the predictive space (All weeks from 04-2014 to 07-2025)
+# Build the input space for the predictive space (All weeks from 04-2014 to 07-2025)
 XXt1 <- fx.iso_week(grid_datetime)
 XXt2 <- fx.sin(grid_datetime)