I am studying machine learning and I am confused by one of the derivations in our textbook. I have two questions:
- what makes equation 3.10 a "exponential of a quadratic function of w"?
- How is the distribution of p(w) derived here?
Here is the relevant excerpt from my textbook:
We begin our discussion of the Bayesian treatment of linear regression by introducing a prior probability distribution over the model parameters w. [...] First note that the likelihood function p(t|w) defined by (3.10) is the exponential of a quadratic function of w. The corresponding conjugate prior is therefore given by a Gaussian distribution of the form