Sequential Testing of Many Simple Hypotheses with Independent Observations

We consider the Bayesian problem of truncated sequential testing of many simple hypotheses with a loss function arbitrarily dependent on the observation step index. We show that, with independent observations, the optimal decision rule is representable as a comparison of the posterior probability for the hypothesis characterized by minimum current posterior risk with a ariable threshold that depends on the posterior probabilities for the other hypotheses. We define the class of cases where this rule remain optimal with dependent observations. We derive an explicit expression for the least posterior risk function, which makes it possible to determine the optimal stopping regions in the case of “far” hypotheses. An example of detection of deterministic signals corrupted by autoregressive noise is considered.