Procedures are considered for testing whether the means of each variable in a sequence of independent random variables can be taken to be the same, against alternatives that a shift might have occurred after some point $r$. Bayesian test statistics as well as some statistics depending on estimates of $r$ are presented and their powers compared. Exact and asymptotic distribution functions are derived for some of the Bayesian statistics.
"On Tests for Detecting Change in Mean." Ann. Statist. 3 (1) 98 - 108, January, 1975. https://doi.org/10.1214/aos/1176343001