**5.2 Marginalization over** *θ*

The main idea here is to consider *θ* as a nuisance parameter. Thus, integrating it out, we get

$$p(\mathbf{f}|\mathbf{g}) = \int p(\mathbf{f}, \theta|\mathbf{g}) \, \mathrm{d}\theta \tag{27}$$

which can be used to infer on *f*. Also, if we still want to get estimates of *θ*, we can first obtain an estimate ^*f* for *f* and then, if needed, to use it as it is illustrated in the following scheme:

$$\begin{array}{|c|c|} \hline \multicolumn{2}{|}{p(f,\theta|g)} \longrightarrow & \multicolumn{2}{|}{p(f|g)} \longrightarrow & \hat{f} \longrightarrow & \multicolumn{2}{|}{p(\theta|\hat{f},g)} \longrightarrow & \hat{\theta} \\ \hline \text{Point Posterior} & \text{Marginalize over } \theta \\ \hline \end{array}$$
