weights added to conjugate regression analysis

Author: HWagn

vignettes/Chapter06.Rmd

@@ -83,7 +83,7 @@ knitr::kable(round(cbind(qt(0.025,df=2*cN)*post.sd+beta.hat, beta.hat,
 We can also plot the marginal posterior distributions.
 ```{r}
 if (pdfplots) {
-  pdf("6-4_1.pdf", width = 8, height = 5)
+  pdf("6-4_1.pdf", width = 8, height = 4)
   par(mar = c(2.5, 1.5, 1.5, .1), mgp = c(1.6, .6, 0))
 }
 par(mfrow = c(1, 3))
@@ -122,7 +122,7 @@ knitr::kable(round(cbind(qt(0.025,df=2*cN)*post.sd.conj+bN.conj, bN.conj,
              col.names=c("2.5 quantile","posterior mean","97.5 quantile"))
          
 ```
-We plot the marginal posteriors together with those under the improper prior.
+We plot the marginal posteriors (in blue) together with those under the improper prior.
 ```{r}
 if (pdfplots) {
   pdf("6-4_2.pdf", width = 8, height = 5)
@@ -138,9 +138,14 @@ for (i in seq_len(nrow(beta.hat))) {
         add=TRUE, col="blue")
 }
 ```
+Compared to the improper prior we see shrinkage to zero under the conjugate prior.
 
 
+```{r}
+W=BN.conj%*%B0.inv.conj
+print(round(W,3))
 
+```
 ## Figure 6.1
 We start with a visualization of the normal and the horseshoe prior.