Marginalization

Is the process of integrating out one of the random variables.

$$p(\mathbf{y})=\int p(\mathbf{x},\mathbf{y})d\mathbf{x}=\underset{=1}{\underbrace{\int p(\mathbf{x}|\mathbf{y})d\mathbf{x}}}p(\mathbf{y})$$

probability