punctuation and plot code

Author: Solomon Kurz

11.Rmd

@@ -1028,7 +1028,7 @@ ggplot(data = tibble(x = seq(from = 0, to = 1, by = .01)),
   theme(plot.background = element_rect(fill = "grey92"))
 ```
 
-McElreath encouraged us to "explore different values for `pbar` and `theta`" (p. 348). Here's a grid of plots with `pbar = c(.25, .5, .75)` and `theta = c(5, 10, 15)`
+McElreath encouraged us to "explore different values for `pbar` and `theta`" (p. 348). Here's a grid of plots with `pbar = c(.25, .5, .75)` and `theta = c(5, 10, 15)`.
 
 ```{r, fig.width = 5, fig.height = 5}
 # data
@@ -1056,12 +1056,14 @@ If you'd like to see how to make a similar plot in terms of $\alpha$ and $\beta$
 
 But remember, we're not fitting a beta model. We're using the beta-binomial. "We're going to bind our linear model to $\bar p$, so that changes in predictor variables change the central tendency of the distribution" (p. 348). The statistical model we'll be fitting follows the form
 
+$$
 \begin{align*}
-\text{admit}_i & \sim \operatorname{BetaBinomial} (n_i, \overline p_i, \theta)\\
-\text{logit} (\overline p_i) & = \alpha \\
+\text{admit}_i & \sim \operatorname{BetaBinomial} (n_i, \bar p_i, \theta)\\
+\text{logit} (\bar p_i) & = \alpha \\
 \alpha                       & \sim \operatorname{Normal} (0, 2) \\
 \theta                       & \sim \operatorname{Exponential} (1).
 \end{align*}
+$$
 
 Here the size $n = \text{applications}$. In case you're confused, yes, our statistical model is not the one McElreath presented at the top of page 348 in the text. If you look closely, the statistical formula he presented does not match up with the one implied by his R code 11.26. Our statistical formula and the `brm()` model we'll be fitting, below, correspond to his R code 11.26.
 
@@ -1274,8 +1276,8 @@ ggplot(data = tibble(x = seq(from = 0, to = 12, by = .01)),
              color = canva_pal("Green fields")(4)[3]) +
   scale_x_continuous(NULL, breaks = c(0, mu, 10)) +
   scale_y_continuous(NULL, breaks = NULL) +
-  coord_cartesian(xlim = 0:10) +
   ggtitle(expression(paste("Our sweet ", gamma, "(3, 1)"))) +
+  coord_cartesian(xlim = 0:10) +
   theme_hc() +
   theme(plot.background = element_rect(fill = "grey92"))
 ```