Wrote some instructions for applying the algorithm

vignettes/aedseo_introduction.Rmd

@@ -134,29 +134,25 @@ sim_data %>%
 
 ## Applying the algorithm
 
+In the following section, the application of the algorithm to the simulated data is outlined. The first step is to transform the simulated data into a `tsibble` object using the `tsd()` function.
 
 ```{r}
-
 # Construct a 'tsibble' object with the time series data
 tsd_data <- tsd(
   observed = simulation$simulation,
   time = dates,
   time_interval = "week"
   )
+```
 
+Next, the time series data object is passed to the `aedseo()` function. Here, a window width of $k=5$ is specified, meaning that a total of 5 weeks is used in the local estimate of the exponential growth rate. Additionally, a 95\% confidence interval is specified. Finally, the exponential growth rate is estimated using quasi-Poisson regression to account for overdispersion in the data.
+
+```{r}
 # Apply the 'aedseo' algorithm
 aedseo_results <- aedseo(tsd = tsd_data, k = 5, level = 0.95, family = "quasipoisson")
-
-# Visualize the growth rate
-aedseo_results %>%
-  ggplot(mapping = aes(x = reference_time, y = growth_rate)) +
-  geom_line() +
-  geom_ribbon(mapping = aes(ymin = lower_growth_rate, ymax = upper_growth_rate), alpha = 0.3) +
-  geom_hline(yintercept = 0, linetype = "dashed") +
-  scale_x_yearweek()
-
 ```
 
+In the figure below, the observed values from the simulations is visualized alongside the local estimate of the growth rate and its corresponding 95\% confidence interval.
 
 
 ```{r}