Properties of Decision Functions Defined by Bans*
- 17 Downloads
Random sequences over a fixed finite alphabet are considered. It is assumed that the sequence is generated by one of m probability distributions on the space of infinite sequences. For a probability measure on the space of infinite sequences a set of projections on a finite number of initial coordinates is considered. The ban of a measure in any projection is defined as a vector having zero probability in this projection.
The problem consists in the search for conditions under which the observations of random sequences on a segment of finite length allow to correctly define the true distribution with probability 1. In the paper, necessary and sufficient conditions are found under which there exists statistical decision determined by bans possessing specified properties. The existence of statistical decisions with specified properties makes them promising for applications in monitoring systems.
Unable to display preview. Download preview PDF.
- 1.S. Axelson, “The base-rate fallacy and its implications for the difficulty of intrusion detection,” in: Proceedings of the 6th Conference on Computer and Communications Security, ASM, New York (1999), pp.1–7.Google Scholar
- 2.N. Bourbaki, Topologie Générale, Nauka, Moscow (1968).Google Scholar
- 4.A. Grusho, N. Grusho, and E. Timonina, “Consistent sequences of tests defined by bans,” in: Springer Proceedings in Mathematics and Statistics, Optimization Theory, Decision Making, and Operation Research Applications, A. Migdalas, A. Sifaleras, C.K. Georgiadis, Y. Papathanasiou, and E. Stiakakis (eds.), Springer, Heidelberg (2013), pp. 281–291.CrossRefGoogle Scholar
- 5.A. Grusho, N. Grusho, and E. Timonina, “Generation of probability measures with the given specification of the smallest bans,” in: Proceedings of 28th European Conference on Modelling and Simulation, Digitaldruck Pirrot GmbHP, Dudweiler, Germany (2014), pp. 565–569.Google Scholar
- 6.A. Grusho, N. Grusho, and E. Timonina, “Statistical decision functions based on bans,” in: Proceedings of the 12th International Conference of Numerical Analysis and Applied Mathematics ICNAAM-2014, AIP Publishing, USA (2014).Google Scholar
- 7.U. V. Prokhorov and U. A. Rozanov, Theory of Probabilities, Nauka, Moscow (1993).Google Scholar