$L_p(\theta) = L(\theta, \hat{\psi})$ where $\hat{\psi}$ maximizes $L$ for a given $\theta$

$L_p(\theta) = \int L(\theta, \psi) d\psi$

$L_p(\theta) = L(\theta, 0)$

$L_p(\theta) = \max_{\theta, \psi} L(\theta, \psi)$