Sector majors BHP Group BHP.AX and Rio Tinto RIO.AX advanced 2.5% and 1.9%, respectively. By Himanshi Akhand July 26 (Reuters) - Australian shares closed higher on Tuesday, supported by mining and energy stocks, even as investors remained cautious ahead of local inflation data and a likely sharp U.S. interest rate hike. Investor focus is on the U.S. Federal Reserve meeting and Australia's inflation data due on Wednesday.