Geodesic
Optimal estimator of hypothesis probability for data mining problems with small samples
International Journal of Applied Mathematics and Computer Science, Tome 22 (2012) no. 3, pp. 629-645.

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The paper presents a new (to the best of the authors' knowledge) estimator of probability called the "[...] completeness estimator" along with a theoretical derivation of its optimality. The estimator is especially suitable for a small number of sample items, which is the feature of many real problems characterized by data insufficiency. The control parameter of the estimator is not assumed in an a priori, subjective way, but was determined on the basis of an optimization criterion (the least absolute errors).The estimator was compared with the universally used frequency estimator of probability and with Cestnik's m-estimator with respect to accuracy. The comparison was realized both theoretically and experimentally. The results show the superiority of the [...] completeness estimator over the frequency estimator for the probability interval ph (0.1, 0.9). The frequency estimator is better for ph [0, 0.1] and ph [0.9, 1].
Keywords: single case problem, probability estimation, frequency interpretation of probability, completeness interpretation of probability, uncertainty theory
Mots-clés : estymacja prawdopodobieństwa, interpretacja częstotliwości prawdopodobieństwa, interpretacja kompletności prawdopodobieństwa, teoria niepewności 
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Piegat, A; Landowski, M. Optimal estimator of hypothesis probability for data mining problems with small samples. International Journal of Applied Mathematics and Computer Science, Tome 22 (2012) no. 3, pp. 629-645. http://geodesic.mathdoc.fr/item/IJAMCS_2012_22_3_a10/

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