

![0_image_0.png](0_image_0.png)

![0_image_1.png](0_image_1.png)

Using the notation introduced in (12),

$$\Gamma_{i,r}(s_{r})\equiv\operatorname{E}_{z|s_{r},C_{i}}\left\{g(z)|s_{r},C_{i}\right\}=\int_{z}g(z)p(z|s_{r},C_{i})\;d z=\int_{z}g(z)\prod_{j}\psi_{i,r}^{j}(z^{j})\;d z$$
$$\mathrm{P}\{C_{i},s_{r}|S\}=\mathrm{P}\{C_{i}|s_{r}\}\ \mathrm{P}\{s_{r}|S\}=\alpha_{i,r}$$

we can write (25) as: