Gamma scale mixture of normal prior

[donotdespair]

Hey @yobin-tim

Please, provide inputs to the Gamma scale mixture of normal section of the doc.

Please include the following parts:

1. State the normal-gamma prior as the hierarchical prior in which the scalar scale premultiplying the covariance matrix of the normal prior for vector $\boldsymbol\alpha$ follows a gamma distribution $$\kappa_{\boldsymbol\alpha}\sim G(s,a)$$
2. Describe briefly a Gibbs sampler in which one step is the normal-ig2 for $\boldsymbol\alpha$ and $\sigma^2$ and the other is the gamma for $\kappa_{\boldsymbol\alpha}$
3. State the GIG full conditional posterior and its parameters
4. Present R code to sample from the GIG distribution using package GIGrvn

Introduce the material using the notation in line with that established in section Autoregressions.

Please, create a Pull Request and include there all your commits containing contributions to this section. In your commits, please, include changes only to the index.qmd file. Could you make your submission clear, making instructive comments on the individual commits? If you're planning to introduce changes to other parts of the website, you're welcome to do that in a separate pull request. This would require you either to play with the branches to which you commit changes in GitHub Desktop, or to wait with introducing changes to other parts of the page later on, when you submit the Pull Request about your section.