Odds algorithm: Difference between revisions

Revision as of 18:42, 27 May 2024

Revision as of 20:16, 10 June 2024

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There exists, in the same spirit, an Odds Theorem for continuous-time arrival processes with [[independent increments]] such as the [[Poisson process]] ({{harvnb|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 estimate]]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 ({{harv|Ferguson (|2008))}}.

== Variations ==

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** "[https://www.cambridge.org/core/journals/journal-of-applied-probability/article/note-on-a-lower-bound-for-the-multiplicative-odds-theorem-of-optimal-stopping/B759B6E4A9D83DB84D6EE1B4C827785B A note on Bounds for the Odds Theorem of Optimal Stopping]", ''[[Annals of Probability]]'' Vol. 31, 1859–1862, (2003).

** "[https://web.archive.org/web/20230409100437/https://www.ems-ph.org/journals/newsletter/pdf/2006-12-62.pdf The art of a right decision]", ''Newsletter of the [[European Mathematical Society]]'', Issue 62, 14–20, (2005).

*{{SfnRef inline|Ferguson|2008}}[[Thomas S. Ferguson|T. S. Ferguson]]: (2008, unpublished)

*{{cite journal |first1=F. T. |last1=Bruss |first2=D. |last2=Paindaveine |title=Selecting a sequence of last successes in independent trials |journal=Journal of Applied Probability |volume=37 |pages=389–399 |year=2000 |issue=2 |doi=10.1239/jap/1014842544 |url=https://mpra.ub.uni-muenchen.de/21166/1/MPRA_paper_21166.pdf}}

*{{Cite journal|last1=Gilbert |first1=J |last2=Mosteller |first2=F |title= Recognizing the Maximum of a Sequence |journal=Journal of the American Statistical Association |volume=61 |pages=35–73 |year=1966 |issue=313 |doi=10.2307/2283044 |jstor=2283044 }}