A methodology for a comprehensive probabilistic tsunami hazard analysis (PTHA) is presented for the major sources of tsunamis (seismic events, landslides, and volcanic activity) and preliminarily applied in the Gulf of Naples (Italy). The methodology uses both a modular procedure to evaluate the tsunami hazard and a Bayesian analysis to include the historical information of the past tsunami events. In the Source module the submarine earthquakes and the submarine mass failures are initially identified in a gridded domain and defined by a set of parameters, producing the sea floor deformations and the corresponding initial tsunami waves. Differently volcanic tsunamis generate sea surface waves caused by pyroclastic density currents from Somma...