Model Extensions: Student-t error term

[donotdespair]

Hey @nathanh93

Please, provide inputs to the Student-t error term section of the doc.

Please include the following parts (make each of them as short as possible, please):

1. Motivate why one would use Student-t error terms in two sentences.
2. Present a univariate Student-t distribution as IG2 scale mixture of a normal distribution
3. Present the necessary extension to the Gibbs sampler briefly using normal-ig2 for $\boldsymbol\alpha$ and $\sigma^2$ and the other is the ig2 for $\lambda$
4. State the IG2 full conditional posterior and its parameters
5. Present R code to sample from the ig2 distribution

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 can 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 to introduce changes to other parts of the page later on when you submit the Pull Request about your section.