Wyniki wyszukiwania - Biblioteka Nauki

1

Information Theory in the mathematical Statistics

100%

Inglot T.

Mathematica Applicanda

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2014

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tom 42

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nr 1

PL

W niniejszym artykule przedstawiony jest zarys teorii informacji z probabilistycznego i statystycznego punktu widzenia. Ten nurt teorii informacji rozwijał się intensywnie w ostatnich dziesięcioleciach. Wpłynął też w znaczący sposób na rozwój metod statystycznych. Celem artykułu jest wprowadzenie czytelnika w przystępny sposób w podaną powyżej tematykę, dostarczenie mu pewnych intuicji i przybliżenie specyfiki podejścia teorio-informacyjnego w statystyce matematycznej.

EN

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 to brief and easy of approach introduction to the main notions of the information theory like entropy, relative entropy (Kullback-Leibler distance), information projection and Fisher information as well as presentation of their most important properties including de Bruijn's identity, Fisher information inequalities and entropy power inequalities. In the short second part we give applications of the notions and results from the first part to limit theorems of the probability theory such as the asymptotic equipartition property, the convergence of empirical measures in the entropy distance, large deviation principle with emphasis to Sanov theorem, the convergence of distributions of homogeneous Markov chains in the entropy distance and the central limit theorem. The main, last part of the article shows some most significant and important applications of the information theory to the mathematical statistics. We discuss connections of the maximum likelihood estimators with the information projections and the notion of sufficient statistic fromthe information-theoretic point of view. The problems of source coding, channel capacity and an amount of information provided by statistical experiments are presented in a statistical framework. Some attention is paid to the expansion of Clarke and Barron and its corollaries e.g. in density estimation. Next, applications of the information theory to hypothesis testing is discussed. We give the classical Stein's Lemma and its generalization to testing composite hypothesis obtained by Bahadur and show their connections with the asymptotic efficiency of statistical tests. Finally, we briefly mention the problem of information criteria in a model seletion including the most popular two-stage minimal description length criterion of Rissanen. The enclosed literature is limited only to papers and books which are referred to in the paper.

2

L Competition for the best student work in the theory of probability and applications of mathematics

63%

Inglot T. , Szajowski K. J.

Mathematica Applicanda

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2016

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tom 44

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nr 2

PL

Oddział Wrocławski Polskiego Towarzystwa Matematycznego organizuje w 2016 r. L(pięćdziesiątą) edycję konkursu mającego na celu propagowanie wśród studentów problematyki teorii prawdopodobieństwa i zastosowań matematyki oraz promocji młodych matematyków uzyskujących oryginalne wyniki teoretyczne czy też rezultaty znajdujące zastosowania w innych dziedzinach nauki lub gospodarki.

EN

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.

3

How powerful are data driven score tests for uniformity

63%

Inglot T. , Janic A.

Applicationes Mathematicae

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2009

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tom 36

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nr 4

375-395

EN

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 shift problem can be measured by the Shannon entropy of a prior distribution. This explains similar behaviour of the average power of our data driven tests.

4

New HPLC method for in vitro dissolution study of antihypertensive mixture amlodipine and perindopril using an experimental design

38%

Gumieniczek A. , Mączka P. , Inglot T. , Pietraś R. , Lewkut E. , Perczak K.

Open Chemistry

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2013

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tom 11

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nr 5

717-724

EN

A new HPLC method was developed for the determination of amlodipine and perindopril in their binary mixture as a part of a routine control of combined formulations. For the first time an HPLC method was used for an in vitro dissolution study of tablets containing the above drugs. The presented method was validated to meet official requirements and this validation included specificity, stability, linearity, precision and accuracy. Chromatography was carried out using a LiChrospher RP-18 column, a mixture containing acetonitrile and phosphate buffer of pH 3.0 (50:50, v/v) as mobile phase and UV detection at 225 nm. The dissolution test was performed using 900 mL of phosphate buffer at pH 5.5 containing 1% cetylpyridini chloride (CPC) at 37°C and 75 rpm, using the paddle method. Robustness procedure was done according to the plan defined by the Plackett-Burman design. The effects of acetonitrile content, pH of the buffer and flow rate of the mobile phase, column temperature, pH and CPC content in the dissolution medium as well as rotation speed of the paddle were considered. After that, both graphical and statistical methods were used for identification of significant and non-significant effects. [...]