  We delve into the in-in formalism and derive general expressions for the
computation of n-point functions for a self-interacting scalar field by means
of a probability density functional (PDF). Even though in typical situations
these formulae are not simpler than the standard approaches to Quantum Field
Theory (QFT), we find that in specific situations, such as a first-order
computation with a non-trivial potential, they can significantly reduce the
effort needed to evaluate quantities of interest. The presented formulae may be
readily generalized to other types of fields (e.g., fermionic Dirac fields),
and to interacting theories that contain various types of fields. An analogous
result for the in-out formalism is presented using the previously employed
strategies. Finally, we apply the obtained results to first-order computations
and work out specific examples where we explore their limitations and possible
prospects for future computations.
