Applications
Applications reach from medical questions in clinical trials over sales problems, secretary problems, portfolio selection, (one-way) search strategies, trajectory problems and the parking problem to problems in on-line maintenance and others.
There exists, in the same spirit, an Odds-Theorem for continuous-time arrival processes with independent increments such as the Poisson process (Bruss (2000)). In some cases, the odds are not necessarily known in advance (as in Example 2 above) so that the application of the odds-algorithm is not directly possible. In this case each step can use sequential estimates of the odds. This is meaningful, if the number of unknown parameters is not large compared with the number n of observations. The question of optimality is then more complicated, however, and requires additional studies. Generalizations of the odds-algorithm allow for different rewards for failing to stop and wrong stops as well as replacing independence assumptions by weaker ones (Ferguson (2008)).
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