What is the test for a pro se petition for writ of habeas under the Antiterrorism and Effective Death Penalty Act?

This petition is governed by the Antiterrorism and Effective Death Penalty Act of 1996, 28 U.S.C. 2254 ("AEDPA"). Under AEDPA, a federal court may not grant a habeas petition regarding any claim adjudicated on the merits in state court unless that adjudication: (1) resulted in a decision that was contrary to, or involved an unreasonable application of clearly established federal law; or (2) resulted in a decision that was based on an unreasonable determination of the facts in light of the evidence presented at the state court proceeding. 28 U.S.C. 2254(d)(1)-(2); Early v. Packer, 537 U.S. 3, 8 (2002). This standard is "highly deferential" and "demands that state-court decisions be given the benefit of the doubt." Cullen v. Pinholster, 563 U.S. 170, 181 (2011) (citations and quotation marks omitted). Moreover, "[t]he petitioner carries the burden of proof," id., though a pro se petition for writ of habeas is construed liberally. Brock v. Weston, 31 F.3d 887, 890 (9th Cir. 1994).