deletions | additions       diff --git a/subsection_Prior_for_Weights_In__.tex b/subsection_Prior_for_Weights_In__.tex  index 3813dae..c7f7b04 100644  --- a/subsection_Prior_for_Weights_In__.tex  +++ b/subsection_Prior_for_Weights_In__.tex 
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In pursuit of generalisability, we adopt the framework that values should be at or near zero with high probability. The most widely used weight-distribution in logistic regression is Guassian, so we take this approach as a useful starting point.  \subsubsection{Guassian Prior: $\mathbf{w} \sim \mathcal{N}(\mathbf{0}, \mathcal{N}_{d\times d}(\mathbf{0},  \text{diag}(\boldsymbol{\sigma}))$} Clearly having a zero mean vector is desirable. Additionally, we have opted to assume that the weights are heteroscedastic but independent of one another. That is, the covariance matrix is a diagonal $d\times d$ matrix $\Sigma = \text{diag}(\boldsymbol{\sigma}) = \text{diag}(\sigma_1, \sigma_2, \dots \sigma_d)$. Consequently,