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## Bayesian Formulation  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:  \begin{align}  P(Y = 1 | \mathbf{X}) &= \sigma(\mathbf{w^TX})//  P(Y = 0 | \mathbf{X}) &= 1 - \sigma(\mathbf{w^TX})\\  &= \sigma(\mathbf{-w^TX})  \end{align}