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Author: HWagn

articles/Chapter06.html

@@ -87,7 +87,8 @@ for (i in seq_len(nrow(beta.hat))) {
 }
 ```
 
-#### 6.2.2 Bayesian Learning under Conjugate Priors
+![](Chapter06_files/figure-html/unnamed-chunk-7-1.png) \### 6.2.2
+Bayesian Learning under Conjugate Priors
 
 Next we consider regression analysis under a conjugate prior. For this
 we define a function that yields the parameters of the posterior
@@ -170,11 +171,11 @@ for (i in seq_len(nrow(beta.hat))) {
 }
 ```
 
-There is little difference to the improper prior for
-$B_{0} = 10\textbf{𝐈}$, however we see shrinkage to zero for
-$B_{0} = \textbf{𝐈}$. The effect of the prior is given by the weight
-matrix $\textbf{𝐖}$, which is computed for the prior
-\$\Normal\\\textbf{0}, \textbf{I}\\\$ below.
+![](Chapter06_files/figure-html/unnamed-chunk-10-1.png) There is little
+difference to the improper prior for $B_{0} = 10\textbf{𝐈}$, however we
+see shrinkage to zero for $B_{0} = \textbf{𝐈}$. The effect of the prior
+is given by the weight matrix $\textbf{𝐖}$, which is computed for the
+prior \$\Normal\\\textbf{0}, \textbf{I}\\\$ below.
 
 ``` r
 W=res_conj2$BN%*%solve(diag(rep(1,d)))
@@ -208,6 +209,8 @@ legend('topright', legend = c("Horseshoe", "Standard normal"), lty = 1:2,
        col = c("blue", "black"))
 ```
 
+![](Chapter06_files/figure-html/unnamed-chunk-12-1.png)
+
 ## Section 6.4
 
 Center the covariates at zero.
@@ -436,6 +439,8 @@ for (i in selection) {
 }
 ```
 
+![](Chapter06_files/figure-html/unnamed-chunk-21-1.png)
+
 We next investigate the trace plots.
 
 ``` r
@@ -481,3 +486,5 @@ for (i in seq_len(ncol(beta.hs))) {
   }
 }
 ```
+
+![](Chapter06_files/figure-html/unnamed-chunk-24-1.png)

articles/Chapter06.md

@@ -11,7 +11,7 @@ articles:
   Chapter07: Chapter07.html
   Chapter08: Chapter08.html
   Chapter09: Chapter09.html
-last_built: 2025-11-11T10:39Z
+last_built: 2025-11-11T10:49Z
 urls:
   reference: https://gregorkastner.github.io/BayesianLearningCode/reference
   article: https://gregorkastner.github.io/BayesianLearningCode/articles