In the paper we present an outline of the information theory from the probabilistic and statistical point of view. Such a direction of the information theory has been intensively developed in recent decades and significantly influenced a progress in the statistical methodology. The aim of the article is to introduce the reader into these problems, provide some intuitions and acquaint with a specific information-theoretic approach to the mathematical statistics.The first part of the paper is devoted...
We construct a new class of data driven tests for uniformity, which have greater average power than existing ones for finite samples. Using a simulation study, we show that these tests as well as some "optimal maximum test" attain an average power close to the optimal Bayes test. Finally, we prove that, in the middle range of the power function, the loss in average power of the "optimal maximum test" with respect to the Neyman-Pearson tests, constructed separately for each alternative, in the Gaussian...
The Wroclaw Branch of the Polish Mathematical Society organizes in 2016 the L (the fifth) edition of the students competition aimed at propagating the theory of probability and applications of mathematics among students and promoting young mathematicians obtaining original theoretical results or results applicable in non-mathematical fields of science or technology.
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