What is it about?

The estimation of probabilities is hard when the number of observations (sample size) is small. What is the definition of sufficiently large sample? How can (subjective) prior probabilities reduce the estimation error? By comparing several probability estimation methods (relative frequency, Laplace's rule of succession, Piegat's formula, the m-estimate) we address these questions within a carefully designed experimental framework in R, which can be publicly accessed from GitHub.

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Why is it important?

In the paper we give the definition of small samples based on the probability estimation error analysis. We compare several probability estimation methods and identify their strengths and weaknesses on small samples. We demonstrate that including prior probabilities in the final probability estimation is beneficial when the difference between the estimated prior and the actual authentic prior is less than 0.3.


The paper presents an in-depth overview of probability estimation methods that are used in data mining, and a framework for evaluation of method's errors. It provides useful contents for data science researchers and practitioners.

Bojan Cestnik

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This page is a summary of: Revisiting the Optimal Probability Estimator from Small Samples for Data Mining, International Journal of Applied Mathematics and Computer Science, December 2019, De Gruyter,
DOI: 10.2478/amcs-2019-0058.
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