Massachusetts Democratic Party chairman John E. Walsh’s decision to leave his post to lead Governor’s Deval Patrick’s political action committee fanned the flames of speculation that the Commonwealth’s chief executive might be taking a look at higher office. But Patrick was clear Tuesday: He is not running to succeed President Obama. “I am not running for president in 2016,” Patrick told reporters at the University of Massachusetts Boston, according to a transcript of his comments provided by his office. “I’m going to finish this second term; I’m going to go back into the private sector,” he said.Joshua Miller can be reached at firstname.lastname@example.org. Follow him on Twitter @jm_bos.