edit horseshoe density plot

Author: HWagn

vignettes/Chapter06.Rmd

@@ -23,7 +23,31 @@ pdfplots <- FALSE # default: FALSE; set this to TRUE only if you like pdf figure
 ```{r, include = FALSE}
 par(mgp = c(1.6, .6, 0), mar = c(2.6, 2.6, 2.6, .4), lwd = 1)
 ```
+
 # Section 6.4
+## Figure 6.1
+We start with a visualization of the normal and the horseshoe prior. 
+
+```{r, echo = -(1:2)}
+if (pdfplots) {
+  pdf("6-4_1.pdf", width = 8, height = 5)
+  par(mar = c(2.5, 1.5, .1, .1), mgp = c(1.6, .6, 0))
+}
+beta <- seq(from=-4, to=4, by=0.01)
+
+# Horseshoe prior
+# approximated by the result of Theorem 1 in Carvalho/Polson (2010)
+c <-  1/sqrt(2*pi^3)
+l <- c/2*log(1+4/beta^2)
+u <- c*log(1+2/beta^2)
+
+plot(beta,(u+l)/2, type="l",ylim=c(0,0.55), xlab=expression(beta),
+     ylab="",lty=1, col="blue")
+lines(beta,dnorm(beta),lty=2) # Standard Normal Prior
+legend('topright', legend=c("Horseshoe", "Standard Normal"), 
+        bty="n",lty=1:2, col=c("blue", "black"))
+```
+
 ## Example 6.1/6.2: Movie data
 
 We use movie data provided within the package to illustrate Bayesian analysis