Mean square error optimal completeness estimator Eph2 of probability

• Autorzy: Piegat A. , Landowski M.
• Języki publikacji: EN

Abstrakty

EN

The paper presents the optimal estimator of probability for the binomial and multinomial case that was called ”completeness estimator Eph2” and theoretical proof of its optimality. The estimator accuracy was compared with accuracy of the universally used frequency estimator. The comparison was realized both theoretically and experimentally. Both comparison ways show superiority of the completeness estimator Eph2 over the frequency estimator frh = nh=n. A prooved solution of the single case problem is given.

Słowa kluczowe

EN

probability; probability estimation; completeness interpretation of probability; probability interpretations; single-case problem

• Wydawca: Komisja Informatyki Polskiej Akademii Nauk, Oddział w Gdańsku
• Czasopismo: Journal of Theoretical and Applied Computer Science
• Rocznik: 2013
• Tom: Vol. 7, nr 3
• Strony: 3--20
• Opis fizyczny: Bibliogr. 20 poz., rys.

Twórcy

autor

Piegat A.

• Faculty of Computer Science and Information Technology, West Pomeranian University of Technology, Szczecin, Poland

autor

Landowski M.

• Institute of Quantitative Methods, Maritime University of Szczecin, Poland

Bibliografia

• [1] Burdzy, K.: The search for certainty. On the clash of science and philosophy of probability. World Scientific, New Jersey, 2009.
• [2] Burdzy, K.: Philosophy of probability. http://www.math.washington.edu/~burdzy/Philosophy/, 2013, online.
• [3] Burdzy, K.: Blog related to the book ”The Search for Certainty. On the Clash of Science and Philosophy of Probability” by K. Burdzy. http://search4certainty.blogspot.com/, 2013, online.
• [4] Carnap, R.: Logical foundations of probability. University Press, Chicago, 1952.
• [5] Chernoff, H.: A measure of asymptotic efficiency for test of a hypothesis based on the sum of observations. Annals of Mathematical Statistics, 23 (4), pp. 493–507, 1952.
• [6] Dubois, D., Prade, H.: Possibility theory. Plenum Press, New York and London, 1988.
• [7] De Finetti, B.: Theory of probability, a critical introductory treatment. Willey, London, 1975.
• [8] Hajek, A.: Interpretations of probability. The Stanford Encyclopedia of Philosophy (Winter 2012 Edition), (ed. E.N. Zalta), http://plato.stanford.edu/ entries/probability-interpret/, 2013, online.
• [9] Khrennikov, A.: Interpretations of probability. Brill Academic Pub. Utrecht, Boston, 1999.
• [10] Klirr, G. J., Yuan, B. (editors): Fuzzy sets, fuzzy logic, and fuzzy systems. Selected papers by Lotfi Zadeh, World Scientific, Singapore, New Jersey, London, Hong Kong, 1996.
• [11] Laplace, P. S.: A philosophical essay on probabilities. English edition, Dover Publication Inc., New York, 1951.
• [12] Larose, D. T.: Discovering statistics. W.H. Freeman and Company, New York, 2010.
• [13] von Mises, R.: Probability, statistics and the truth. Macmillan, second revised English edition, Dover, New York, 1957.
• [14] Piegat, A.: Uncertainty of probability. In Recent Advances in Fuzzy Sets, Intuitionistic Fuzzy Sets, Generalized Nets and Related Topics, Volume 1: Foundations, Systems Research Institute, Polish Academy of Sciences, Warsaw, pp. 159–173, 2011.
• [15] Piegat, A.: Basic lecture on completeness interpretation of probability. http://kmsiims.wi.zut.edu.pl/ pobierz-pliki/ cat view/47-publikacje, 2011, online.
• [16] Popper, K. R.: The propensity interpretation of the calculus of probability and the quantum theory, In Observation and Interpretation: A Symposium of Philosophers and Physicists (eds S. Korner), London: Butterworth Scientific Publications, pp. 65–70, 1957.
• [17] Rocchi, P.: The structural theory of probability: new ideas from computer science on the ancient problem of probability interpretation. Kluwer Academic/Plenum Publishers, New York, 2003.
• [18] Shafer, G.: A mathematical theory of evidence. Princetown University Press, Princetown and London, 1976.
• [19] Yakov, B. H.: Info-gap decision theory. Second edition, Elsevier, Oxford, Amsterdam, 2006.
• [20] Zadeh, L. A.: Fuzzysets. Information and Control, Vol.8, pp. 338–353, 1965.