deletions | additions       diff --git a/Vague_Outline_Slice_Sampling_Slice__.md b/Vague_Outline_Slice_Sampling_Slice__.md  index ecc3cd7..9c0981e 100644  --- a/Vague_Outline_Slice_Sampling_Slice__.md  +++ b/Vague_Outline_Slice_Sampling_Slice__.md 
...
Define the logistic sigmoid function \(\sigma(\alpha) = \frac{1}{1 + \exp(-\alpha)}\). A logistic regression models a binary-response variable with the following density function:  $$P(Y \begin{align}  P(Y  = 1 | X) \mathbf{X}) &= \sigma(\mathbf{w^TX})\\  P(Y  = \sigma(\mathbf{w^TX})$$ 0 | \mathbf{X}) &= 1 - \sigma(\mathbf{w^TX})\\  &= \sigma(\mathbf{-w^TX})  \end{align}