This paper presents a Bayesian framework to estimate joint, conditional, and marginal probabilities in directed acyclic graphs to study the progression of hospitalized patients with confrmed severe infuenza. Using data from the PIDIRAC retrospective cohort in Catalonia, we model patient pathways from admission to discharge, death, or transfer. Transition probabilities are estimated using a Bayesian Dirichlet-multinomial approach, while posterior distributions for absorbing states or inverse probabilities are assessed via simulation. Bayesian methodology quantifes uncertainty through posterior distributions, offering insights into disease progression and in improving hospital planning. These fndings support more effective patient management and informed decision making during seasonal infuenza outbreaks.