I'm currently working on an assigment and I'm currently stuck and could really use some help, I've been given the fact that my prior over my parameters W is given by a gaussian pdf, likewise is the likelihood a gaussian pdf. Without any further proof the posterior can also be taken for a gaussian.

My expression for the posterior is:

$$p(\textbf{W}\vert \textbf{X},\textbf{T}) = \exp(-\frac{1}{2}\textbf{W}^{T}\Sigma_w^{-1}\textbf{W} +\textbf{W}^{T}\Sigma_w^{-1}\textbf{W}_\mu -\frac{1}{2}\textbf{W}_\mu^{T}\Sigma_w^{-1}\textbf{W}_\mu)$$

I've made derivations for the mean $\textbf{W}_\mu$ and the covariance $\Sigma_w^{-1}$, but I don't think they play an important role to what I'm supposed to do here. I think I should use maximum likelihood but I don't seem to get the calculations right.


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