deletions | additions       diff --git a/subsection_Prior_for_Weights_In__.tex b/subsection_Prior_for_Weights_In__.tex  index dc8c09b..0fe458b 100644  --- a/subsection_Prior_for_Weights_In__.tex  +++ b/subsection_Prior_for_Weights_In__.tex 
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\subsubsection{Guassian Prior: $\mathbf{w} \sim \mathcal{N}_{d\times d}(\mathbf{0}, \text{diag}(\boldsymbol{\sigma}))$}  A zero-mean vector is an obvious starting point. Additionally, we have opted to assume that the weights are heteroscedastic but independent of one another. That is, the covariancematrix  is a diagonal $d\times d$ matrix  $\Sigma = \text{diag}(\boldsymbol{\sigma}) = \text{diag}(\sigma_1, \sigma_2, \dots \sigma_d)$. Consequently, $$p(\mathbf{w} | \boldsymbol{\sigma}) = (2\pi )^{-\frac{d}{2}} | \Sigma | ^{-\frac{1}{2}} \exp(-\frac{1}{2} \mathbf{w^T} \Sigma ^{-1} \mathbf{w})$$