Concluding Remarks

V. I. Ivanenko ()
Additional contact information
V. I. Ivanenko: Kyviv Polytechnic Institute

Chapter Chapter 9 in Decision Systems and Nonstochastic Randomness, 2010, pp 205-208 from Springer

Abstract: Abstract Decision-making under uncertainty accompanies all human activity, and so it is difficult to locate the beginnings of research in this field. At any rate, the consideration of problems in which nothing was known about the parameter but the set of its possible values—total uncertainty problems—can be found already in the work of Johann Bernoulli, Laplace, and Bayes alongside problems in which the unknown parameter was random with a given distribution. However, the “principle of insufficient foundation” (Bayes postulate) suggested therein, which in the case of total uncertainty recommended the consideration of all values of the unknown parameter as equiprobable, eventually proved to be logically inconsistent, and in 1854 it was subjected to serious criticism by J. Bull [29]. Attempts to save this principle by a formalization of conditions under which it does not lead to contradictions (see, for example, [10]) were undertaken later, but the overwhelming majority of researchers preferred to eschew the principle entirely, and as a result, quite a number of approaches to problems with uncertainty appeared.

Keywords: Unknown Parameter; Decision System; Average Loss; Information Quantity; Adaptive Control System (search for similar items in EconPapers)
Date: 2010
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4419-5548-7_9

Ordering information: This item can be ordered from
http://www.springer.com/9781441955487

DOI: 10.1007/978-1-4419-5548-7_9

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().