16 Math Testing

$$p(\theta |y)=\frac{p(y|\theta )p(\theta )}{p(y)}$$

$$\begin{array}{rl}p({\theta }_h|y)=& \int \cdots \int p({\theta }_1,\dots ,{\theta }_h,\dots ,{\theta }_H|y)d{\theta }_{\setminus h}\\ =& \int \cdots \int p({\theta }_h|{\theta }_{\setminus h},y)p({\theta }_{\setminus h}|y)d{\theta }_{\setminus h}\end{array}$$

$$\begin{gathered} a^2=b^2+c^2 \\ {\eta }_i|\alpha ,\beta \sim \text{Gamma}(\alpha +\xi ,\beta +\chi ),i=1,\dots ,N \\ \alpha ,\beta \sim \mathcal{I}\mathcal{G}(0.5,0.05) \end{gathered}$$