The maximum of a sequence with prior information

Let X1...,Xn denote a random sample of size n form distribution function F. The X's are observed one at a time in sequence; the problem is to stop at a maximum of the n observations, where recall is not permitted and where the loss is 0 if a maximum is selected and 1 if not. Here it is assumed that the distribution function is from a Dirichlet process with known parameter. Sequential stopping rules are developed and the probabilities of maximal selection computed. robustness of the procedure is investigated in an example.