Arlotto, AlessandroSteele, John. M2023-05-232023-05-232011-11-012016-07-01https://repository.upenn.edu/handle/20.500.14332/42141We consider the problem of selecting sequentially a unimodal subsequence from a sequence of independent identically distributed random variables, and we find that a person doing optimal sequential selection does so within a factor of the square root of two as well as a prophet who knows all of the random observations in advance of any selections. Our analysis applies in fact to selections of subsequences that have d+1 monotone blocks, and, by including the case d= 0, our analysis also covers monotone subsequences.MathematicsArticle