What is the evidence that the bones found under St. Peter's Basilica are actually St. Peter's bones?

There were some bone fragments found under St. Peter's Basilica in the 1940's. Pope Paul VI said in 1968 that the bones were "identified in a way that we can consider convincing." What is the convincing argument that these bones are indeed's St. Peter's? A perfect answer will include the details about how the bones were found. ___ On a related note, the bones have recently been made available for public viewing for the first time . During a Mass, Pope Francis seemed to venerate the relics, which may mean that the Church will officially declare them as St. Peter's bones.