Odds algorithm: Difference between revisions

Revision as of 16:03, 30 May 2011

Revision as of 19:58, 10 July 2011

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Applications reach from medical questions in [[clinical trial]]s over sales problems, [[secretary problems]], [[portfolio (finance)|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 estimatesestimate]]s 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)).