What is the standard for federal judges to grant a habeas relief under the AEDPA?

the standard we are bound to apply, even if we are convinced that the habeas petitioner's constitutional rights were violated. See Cavazos v. Smith, U.S. , 132 S.Ct. 2, 4, 181 L.Ed.2d 311 (2011) (per curiam) ([T]he inevitable consequence of [AEDPA] is that [federal] judges will sometimes encounter convictions that they believe to be mistaken, but that they must nonetheless uphold.); see also Brown v. Payton, 544 U.S. 133, 14849, 125 S.Ct. 1432, 161 L.Ed.2d 334 (2005) (Breyer, J., concurring) (stating that even though he likely would have found a constitutional violation [w]ere [he] a California state judge, the state court's denial of habeas relief was reasonable).