  Suppose we observe a Poisson process in real time for which the intensity may
take on two possible values $\lambda_0$ and $\lambda_1$. Suppose further that
the priori probability of the true intensity is not given. We solve a minimax
version of Bayesian problem of sequential testing of two simple hypotheses to
minimize a linear combination of the probability of wrong detection and the
expected waiting time in the worst scenario of all possible priori
distributions. An equivalent characterization for the least favorable
distributions is derived and a sufficient condition for the existence is
concluded.
