# Typo in the definition of Finite Mixed Model in Machine Learning a probabilistic Perspective

In subsection 25.2.1 it's stated, regarding finite mixture model:

The usual representation (of a finite mixture model) is as follows:

$$p(x_i|z_i = k, \boldsymbol\theta) = p(x_i|\boldsymbol\theta_k)$$

$$p(z_i = k| \boldsymbol\pi = \pi_k) = \pi_k$$

$$p(\boldsymbol\pi|\alpha) =\text{Dir}(\boldsymbol\pi|(\alpha/K)\boldsymbol1_K)$$

The form of $$p(\boldsymbol\theta_k|\lambda)$$ is chosen to be be conjugate to $$p(x_i|\boldsymbol\theta_k)$$. We can write $$p(x_i|\boldsymbol\theta_k)$$ as $$\boldsymbol{x}_i \sim F(\boldsymbol\theta_{z_i})$$ where F is the observation distribution. Similarly, we can write $$\boldsymbol\theta_k \sim H(\lambda)$$, where H is the prior.

I don't agree on

We can write $$p(x_i|\boldsymbol\theta_k)$$ as $$\boldsymbol{x}_i \sim F(\boldsymbol\theta_{z_i})$$ where F is the observation distribution

Because $$F(\boldsymbol\theta_{z_i})$$ is the conditional probability of x given z. So in my opinion it should be:

We can write $$p(x_i|\boldsymbol\theta_k)$$ as $$\boldsymbol{x}_i|z_i \sim F(\boldsymbol\theta_{z_i})$$ where F is the observation distribution

• Correct, this is the conditional distribution. – Xi'an Jan 11 at 13:29