new example: yearly maxima

Author: gregorkastner

vignettes/Chapter09.Rmd

@@ -242,3 +242,36 @@ abline(h = q_normal, col = 4, lty = 1, lwd = 1.5)
 abline(h = q_t, col = 2, lty = 2, lwd = 1.5)
 legend("topleft", c("Normal", "Student t"), lty = 1:2, col = c(4,2), lwd = 1.5)
 ```
+
+
+## Example 9.9: Predicting yearly maxima for the road safety data
+
+We use a sampling-based approach to obtain draws from posterior predictive
+by first drawing from the posterior $\mu|\mathbb{y} \sim \mathcal{G}(a_N, b_N)$.
+Then, using these draws as mean parameters for the Poisson likelihood, we draw
+12 times each to obtain yearly predictions. Of these, we take the maxima.
+
+```{r}
+set.seed(1)
+y <- accidents[, "seniors_accidents"]
+aN <- sum(y) + 1
+bN <- length(y)
+mus <- rgamma(ndraws, aN, bN)
+yfs <- matrix(rpois(12 * ndraws, mus), ncol = 12)
+Us <- apply(yfs, 1, max)
+```
+
+Now we visualize.
+
+```{r, echo = -c(1:2)}
+if (pdfplots) {
+  pdf("9-1_5.pdf", width = 10, height = 4)
+  par(mar = c(2.5, 1.5, .1, .1), mgp = c(1.6, .6, 0))
+}
+par(mfrow = c(1, 2))
+plot(tab <- proportions(table(Us)), xlab = "U", ylab = "")
+plot(as.table(cumsum(tab)), type = "h", xlab = "U", ylab = "")
+probs <- c(0.025, 0.975)
+abline(h = probs, lty = 3)
+mtext(probs, side = 2, at = probs, adj = c(0, 1), cex = .8, col = "dimgrey")
+```