deletions | additions       diff --git a/subsection_Prior_for_Weights_In__.tex b/subsection_Prior_for_Weights_In__.tex  index 743c469..ef9b828 100644  --- a/subsection_Prior_for_Weights_In__.tex  +++ b/subsection_Prior_for_Weights_In__.tex 
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Using this information, it can be shown that finding the MAP estimator of $\mathbf{w}$ is equivalent to solving the maximum likelihood problem with a ridge regularisation parameter \cite{Hoerl_1970}. The success and ubiquity of this approach then speaks to the reasonableness of assuming Guassian priors. That is,  \begin{align}  \hat{\mathbf{w}} &= \text{argmax}_\mathbf{w} \log \left( \left\{  L(\mathbf{w} \mid \mathcal{D})\times p(\mathbf{w} \mid \boldsymbol{\sigma} )\right)\\ )\right\}\\  & = \text{argmax}_\mathbf{w} \log(L(\mathbf{w} \mid \mathcal{D})) + \log p(\mathbf{w} \mid \boldsymbol{\sigma})\\  & := \text{argmax}_\mathbf{w} \mathcal{l}(\mathbf{w} \mid \mathcal{D}) - (\mathbf{w}^T \boldsymbol{\sigma^{-1}})^2  \end{align}