typos fixed

Author: bettinagruen

vignettes/Chapter05.Rmd

@@ -1,4 +1,4 @@
----
+'---
 title: "Chapter 5: Learning More About Bayesian Learning"
 output: rmarkdown::html_vignette
 vignette: >
@@ -28,7 +28,7 @@ par(mgp = c(1.6, .6, 0), mar = c(2.6, 2.6, 2.6, .4), lwd = 1)
 ## Example 5.3 / Figure 5.1: The adaptive nature of Bayesian learning
 
 We illustrate the adaptive nature of Bayesian learning (also referred to
-as *sequential updating* or *on-line learning*) via the beta-Bernoulli model
+as *sequential updating* or *on-line learning*) via the Beta-Bernoulli model
 from earlier.
 
 ```{r, echo=-(1:2)}
@@ -56,7 +56,7 @@ for (i in seq_along(thetatrue)) {
     lines(theta, dbeta(theta, a0 + succ, b0 + fail), col = rgb(0, 0, 0, .2 + .4*j/N))
   }
   
-  legend('topright', paste("N =", c(0, 20, 40, 60, 80, 100)), lty = 1,
+  legend("topright", paste("N =", c(0, 20, 40, 60, 80, 100)), lty = 1,
          col = rgb(0, 0, 0, .2 + .4*c(0, 20, 40, 60, 80, 100)/N))
 }
 ```
@@ -264,7 +264,7 @@ abline(h = e, lty = 2)
 ## Figure 5.4: Bayesian asymptotics 1
 
 To reproduce this figure, we again re-use the theory from Chapter 3 (the
-beta-Bernoulli model).
+Beta-Bernoulli model).
 
 ```{r, echo=-(1:2)}
 if (pdfplots) {
@@ -376,7 +376,7 @@ We now compute various point estimates under several settings. Note that we
 use the same number of 1s ($S_N$) as before.
 
 ```{r}
-options(knitr.kable.NA = '')
+options(knitr.kable.NA = "")
 a0 <- c(1, 2)
 b0 <- c(1, 4)
 set <- expand.grid(N = N, thetatrue = thetatrue, a0 = a0)
@@ -427,7 +427,7 @@ res <- cbind(res[,1:3], leftconf, rightconf, leftHPD, rightHPD)
 knitr::kable(round(res, 3))
 ```
 
-## Example 5.10 / Table 5.3: Coverage probabilities under the beta-Bernoulli model
+## Example 5.10 / Table 5.3: Coverage probabilities under the Beta-Bernoulli model
 For a (frequentist) estimate of the coverage probabilities, we simulate
 many data sets for each of the parameter configurations and check how often
 the intervals contain the true parameter.
@@ -486,7 +486,7 @@ res <- cbind(res[,1:2],
 knitr::kable(round(res, 2))
 ```
 
-## Example 5.11: Coverage probabilities under the Poisson-gamma model
+## Example 5.11: Coverage probabilities under the Poisson-Gamma model
 
 As above, but for data from a $\mathcal{P}(5)$-distribution. We
 estimate the mean from $N = 24$ data points and construct CIs.
@@ -517,7 +517,7 @@ rightconf2 <- means + qnorm(1 - alpha / 2) * sqrt(vars / N)
 inconf2 <- leftconf2 <= mutrue & mutrue <= rightconf2
 ```
 
-For the Baysian variants, we look compute the equal-tailed and the HPD intervals.
+For the Bayesian variants, we compute the equal-tailed and the HPD intervals.
 
 ```{r}
 leftequal <- qgamma(alpha / 2, N * means + 1, N)