Sequential probability ratio test ($S_t={\sum }_{s=1}^t\log [f_1(Y_s)/f_0(Y_s)]$)

A sequential probability ratio test accumulates the log-likelihood ratio for two specified simple statistical hypotheses until it reaches an upper or lower boundary. An upper crossing favors the alternative, a lower crossing favors the null, and observations continue between them. Error-calibrated boundaries are approximately $\log [(1-\beta )/\alpha ]$ and $\log [\beta /(1-\alpha )]$; discrete overshoot means these approximations need calibration.