Titlebook: Universal Coding and Order Identification by Model Selection Methods; élisabeth Gassiat Book 2018 Springer International Publishing AG, pa

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Book 2018o 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

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1439-7382 nd statistical inference.Presents applications to order idenThe 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

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Universal Coding on Infinite Alphabets,se results are asymptotic. By a “huge alphabet”, we mean for instance that within the data, some letters may not have occurred yet. To understand how to cope with such situations, we will be interested in the case where the alphabet is infinite. In a finite alphabet, we have seen that there exist un

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Model Order Estimation,compromise between model complexity and adequacy to the data. Different types of adequacy to data can be used, according to the question one is interested in. In some applications, the model order is a structural parameter with a precise interpretation regarding the phenomenon being studied. Here, w

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Book 2018ession 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 Sha

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