• The set of {𝑦₁, 𝑦₂, …, 𝑦_𝑛} independent given 𝑤
• $y_i=N(w^T{x}_i,a^{-1})$

where:

• $a>0$

• $\mathbf{P}(w)=N(0,b^{-1}I)$
• $\mathbf{P}(w)\propto exp(-\frac{b}{2}{w}^{T}w)$

where:

• $b>0$

• $\mathbf{P}(D|w)\propto exp\left(-\frac{a}{2}(y-Xw{)}^T(y-Xw)\right)$

where:

• $X=\left[\begin{array}{c}-x_1-\\ -x_2-\\ ⋮\\ -x_n-\end{array}\right]$
• $y=\left[\begin{array}{c}{y}_1\\ y_2\\ ⋮\\ y_n\end{array}\right]$

• $\mathbf{P}(w|D)\propto \mathbf{P}(D|w)\mathbf{P}(w)$
• $\mathbf{P}(w|D)\propto exp\left(-\frac{a}{2}(y-Xw{)}^T(y-Xw)\right)\mathbf{P}(w)$
• $\mathbf{P}(w|D)\propto exp\left(-\frac{a}{2}(y-Xw{)}^T(y-Xw)\right)exp(-\frac{b}{2}{w}^{T}w)$
• $\mathbf{P}(w|D)\propto exp\left(-\frac{a}{2}(y-Xw{)}^T(y-Xw)-\frac{b}{2}{w}^{T}w\right)$
• TODO
• https://www.youtube.com/watch?v=nrd4AnDLR3U