Ramón Alvarez-Esteban, Olga Valencia, Mónica Bécue-Bertaut's Advances in Data Analysis: Theory and Applications to PDF

By Ramón Alvarez-Esteban, Olga Valencia, Mónica Bécue-Bertaut (auth.), Christos H. Skiadas (eds.)

ISBN-10: 0817647988

ISBN-13: 9780817647988

ISBN-10: 0817647996

ISBN-13: 9780817647995

An outgrowth of the 12th foreign convention on utilized Stochastic types and knowledge research, this ebook is a suite of invited chapters providing contemporary advancements within the box of information research, with purposes to reliability and inference, facts mining, bioinformatics, lifetime info, and neural networks. emphasised through the quantity are new tools with the possibility of fixing real-world difficulties in numerous areas.

The e-book is split into 8 significant sections:

* facts Mining and textual content Mining

* info thought and Statistical Applications

* Asymptotic Behaviour of Stochastic methods and Random Fields

* Bioinformatics and Markov Chains

* existence desk facts, Survival research, and hazard in family Insurance

* Neural Networks and Self-Organizing Maps

* Parametric and Nonparametric Statistics

* Statistical conception and Methods

Advances in information Analysis is an invaluable reference for graduate scholars, researchers, and practitioners in records, arithmetic, engineering, economics, social technology, bioengineering, and bioscience.

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Extra info for Advances in Data Analysis: Theory and Applications to Reliability and Inference, Data Mining, Bioinformatics, Lifetime Data, and Neural Networks

Example text

A general result which would hold for all existing sources is certainly unexpected. This is why we introduce a condition on the source for each frequency threshold. Both conditions only concern the words produced and not the way they are produced. Hence, the source may be nonexplicit. 4 that both conditions are natural since they are verified by a large class of sources, classical or not. In the whole section, m and n, respectively, denote the number of questions and persons in a random database B.

The operators Gw are fundamental since the probability pw that a word begins by w satisfies pw = f0 (t)dt = Iw Gw [f0 ](t)dt. I In particular, the probability pw1 ·w2 (here · is the concatenation) expresses with the operator Gw1 ·w2 = Gw2 ◦ Gw1 . Note that this functional relation replaces the wellknown properties pw1 ·w2 = pw1 · pw2 valid only for memoryless sources. 40 L. Lhote Now, fix W1 and W2 two sets of words. By additivity, the probability that a word belongs to W1 · W2 [words w1 · w2 with (w1 , w2 ) ∈ W1 × W2 ] is related to the operator GW1 ·W2 = GW2 ◦ GW1 with GW = Gw .

This class is then a good candidate for generating general databases that we call dynamical databases. We prove the following. Theorem 3. A (Markovian and irreducible) dynamical source satisfies Condition 1 and, for all γ ≥ 1, Condition 2-γ. Moreover, Σγ,m is of the form: −m Σm,γ = κγ · λm γ (1 + O(θγ )), κγ > 0, λγ > 1, θγ > 1 and λγ > λγ+1 . In particular, Theorems 1 and 2 hold for (Markovian and irreducible) dynamical databases. 2 describes some instances of dynamical sources. A dynamical source emits symbols in the following way.

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Advances in Data Analysis: Theory and Applications to Reliability and Inference, Data Mining, Bioinformatics, Lifetime Data, and Neural Networks by Ramón Alvarez-Esteban, Olga Valencia, Mónica Bécue-Bertaut (auth.), Christos H. Skiadas (eds.)


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