Abstract The web is a source of a large amount of arguments and their acceptability statuses (e.g., votes for and against the arguments). However, relations existing between the fore-mentioned arguments are typically not available. This study investigates the utilisation of acceptability semantics to statistically estimate an attack relation between arguments wherein the acceptability statuses of arguments are provided. A Bayesian network model of argument-based reasoning is defined in which Dung’s theory of abstract argumentation gives the substance of Bayesian inference. The model correctness is demonstrated by analysing properties of estimated attack relations and illustrating its applicability to online forums.