Universal Coding and Order Identification by Model Selection Methods

Lingua: inglese

Editore: Springer International Publishing Dez 2018, 2018

3030071677 / 9783030071677

Serie: Libro 153 di 187 - Springer Monographs in Mathematics

Da: BuchWeltWeit Ludwig Meier e.K., Bergisch Gladbach, GermaniaBuchWeltWeit Ludwig Meier e.K.

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This item is printed on demand - it takes 3-4 days longer - Neuware -The purpose of these notes is to highlight the far-reaching connections between Information Theory and Statistics. Universal coding and adaptive compression are indeed closely related to statistical inference concerning processes and using maximum likelihood or Bayesian methods. The book is divided into four chapters, the first of which introduces readers to lossless coding, provides an intrinsic lower bound on the codeword length in terms of Shannon's entropy, and presents some coding methods that can achieve this lower bound, provided the source distribution is known. In turn, Chapter 2 addresses universal coding on finite alphabets, and seeks to find coding procedures that can achieve the optimal compression rate, regardless of the source distribution. It also quantifies the speed of convergence of the compression rate to the source entropy rate. These powerful results do not extend to infinite alphabets. In Chapter 3, it is shown that there are no universal codes over the class of stationary ergodic sources over a countable alphabet. This negative result prompts at least two different approaches: the introduction of smaller sub-classes of sources known as envelope classes, over which adaptive coding may be feasible, and the redefinition of the performance criterion by focusing on compressing the message pattern. Finally, Chapter 4 deals with the question of order identification in statistics. This question belongs to the class of model selection problems and arises in various practical situations in which the goal is to identify an integer characterizing the model: the length of dependency for a Markov chain, number of hidden states for a hidden Markov chain, and number of populations for a population mixture. The coding ideas and techniques developed in previous chapters allow us to obtain new results in this area.This book is accessible to anyone with a graduate level in Mathematics, and will appeal to information theoreticians and mathematical statisticians alike. Except for Chapter 4, all proofs are detailed and all tools needed to understand the text are reviewed. 164 pp. Englisch.…

Codice articolo 9783030071677

Titolo
Universal Coding and Order Identification by Model Selection Methods
Autore
Élisabeth Gassiat
Editore
Springer International Publishing Dez 2018
Anno di pubblicazione
2018
Condizione
Neu
Rilegatura
Taschenbuch
Lingua
inglese
ISBN 10
3030071677
ISBN 13
9783030071677
Peso dell'articolo
260 grammi
Dimensioni
235x155x10 mm
Serie
Libro 153 di 187: Springer Monographs in Mathematics

BuchWeltWeit Ludwig Meier e.K.

Bergisch Gladbach, Germania

Venditore con 5 stelle

Venditore AbeBooks dal 11 gennaio 2012

Tariffe di spedizione da Germania a U.S.A.

ArticoloDa 5 a 15 giorni lavorativiDa 5 a 15 giorni lavorativi
Primo articoloEUR 23,00EUR 23,00
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BuchWeltWeit Ludwig Meier e.K.

Germania