Question

Now let's consider the fully Bayesian version of regression, with the same assumptions as in (c), i.e. $\Gamma = \alpha I$ and $\Sigma = \sigma^2 I$. This formulation is the linear version of Gaussian process regression.

(d) What happens to the mean and covariance of the posterior $p(\theta|\mathcal{D})$ for different values of $\alpha$ and $\sigma^2$ (e.g., $\alpha = 0, \alpha \to \infty, \sigma^2 = 0$)?