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Titlebook: Information and Complexity in Statistical Modeling; Jorma Rissanen Book 2007 Springer-Verlag New York 2007 Excel.Information.Minimum Descr

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书目名称Information and Complexity in Statistical Modeling
编辑Jorma Rissanen
视频video
概述The author is a distinguished scientist in information theory and statistical modeling
丛书名称Information Science and Statistics
图书封面Titlebook: Information and Complexity in Statistical Modeling;  Jorma Rissanen Book 2007 Springer-Verlag New York 2007 Excel.Information.Minimum Descr
描述.No statistical model is "true" or "false," "right" or "wrong"; the models just have varying performance, which can be assessed. The main theme in this book is to teach modeling based on the principle that the objective is to extract the information from data that can be learned with suggested classes of probability models. The intuitive and fundamental concepts of complexity, learnable information, and noise are formalized, which provides a firm information theoretic foundation for statistical modeling. Inspired by Kolmogorov‘s structure function in the algorithmic theory of complexity, this is accomplished by finding the shortest code length, called the stochastic complexity, with which the data can be encoded when advantage is taken of the models in a suggested class, which amounts to the MDL (Minimum Description Length) principle. The complexity, in turn, breaks up into the shortest code length for the optimal model in a set of models that can be optimally distinguished from the given data and the rest, which defines "noise" as the incompressible part in the data without useful information....Such a view of the modeling problem permits a unified treatment of any type of paramet
出版日期Book 2007
关键词Excel; Information; Minimum Description Length; Shannon; Signal; algorithm; algorithms; bioinformatics; calc
版次1
doihttps://doi.org/10.1007/978-0-387-68812-1
isbn_softcover978-1-4419-2267-0
isbn_ebook978-0-387-68812-1Series ISSN 1613-9011 Series E-ISSN 2197-4128
issn_series 1613-9011
copyrightSpringer-Verlag New York 2007
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Stochastic Complexitys in the algorithmic theory, the complexity is the primary notion, which then allows us to define the more intricate notion of information. Our plan is to define the complexity in terms of the shortest code length when the data is encoded with a class of models as codes. In the previous section we s
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Structure Functionity. For this we have to construct the analog of Kolmogorov complexity and to generalize Kolmogorov’s model as a finite set to a statistical model. The Kolmogorov complexity .(.) will be replaced by the . for the model class .. (5.40) and the other analogs required will be discussed next. In this se
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Optimally Distinguishable Modelsmaximal number of . models that can be obtained from data of size .. His idea of distinguishability is based on differential geometry and is somewhat intricate, mainly because it is defined in terms of covers of the parameter space rather than partitions. The fact is that any two models . and ., no
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Applicationsis the true data-generating distribution. This means that the theory does not take into account the effect of having to fit the hypotheses as models to data, and hence whatever has been deduced must have a fundamental defect. The second fundamental flaw in the theory is that there is no rational qua
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