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Rissanen J. — Information and complexity in statistical modeling

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Название: Information and complexity in statistical modeling

Автор: Rissanen J.

Аннотация:

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 parameters, their number, and even their structure. Since only optimally distinguished models are worthy of testing, we get a logically sound and straightforward treatment of hypothesis testing, in which for the first time the confidence in the test result can be assessed. Although the prerequisites include only basic probability calculus and statistics, a moderate level of mathematical proficiency would be beneficial. The different and logically unassailable view of statistical modelling should provide excellent grounds for further research and suggest topics for graduate students in all fields of modern engineering, including and not restricted to signal and image processing, bioinformatics, pattern recognition, and machine learning to mention just a few.

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Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

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Год издания: 2007

Количество страниц: 145

Добавлена в каталог: 08.12.2013

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Предметный указатель
 AIC      44 Alphabet      9 ARMA      126 Bayes      4 6 BIC      5 6 100 Chain rules      21 Channel capacity      19 Code      9 Code, arithmetic      34 Code, concatenation      9 Code, Huffman      11 Code, length      6 Code, Tunstall      32 Codeword      9 complexity      VII 3 Complexity, algorithmic      53 Complexity, stochastic      76 Confidence index      106 confidence intervals      92 context      108 Criterion, AIC      44 Criterion, BIC      VIII 5 6 Criterion, MDL      6 98 Criterion, PMDL      69 Critical region      103 Distinguishable      2 89 entropy      12 Equipartition property      25 Error      112 Exponential family      58 Fisher information matrix      62 Fisher information matrix, empirical      63 histogram      123 Hypothesis      103 Hypothesis, composite      103 Hypothesis, null      103 IID      13 Index of confidence      106 information      VII 8 Information, algorithmic      3 55 Information, Fisher      62 Information, learnable      85 Information, mutual      18 Jensen's inequality      22 Kolmogorov, minimal sufficient statistics      54 Kolmogorov, structure function      52 Kraft-inequality      10 Kullback — Leibler distance      62 level of significance      104 Markov process      29 MDL principle      97 Message      9 ML principle      VIII Model      57 Model, -class      60 Model, class      57 Model, exponential      58 Model, universal algorithmic      60 Model, universal mixture      62 Model, universal NML      64 Model, universal predictive      67 Model, universal tree machine      106 Noise      99 Ockham's razor      VIII Posterior      4 98 Power      103 Predictive MDL principle      70 Prefix      10 Prefix, code      10 Prefix, property      10 Prequential      77 Prior      14 15 Prior for integers      26 Prior, canonical      65 Prior, Jeffreys'      82 Prior, noninformative      82 Random process      27 Relative entropy      18 Stationary      28 Stirling's approximation      86 Structure index      5 Sufficient statistics      54 Symbol      9 Theory of types      23 Time-invariant      29 True distribution      3 Universal, coding      38 Universal, model      60 Universal, prior for integers      14
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