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Rissanen J. — Information and complexity in statistical modeling
Rissanen J. — Information and complexity in statistical modeling

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Название: Information and complexity in statistical modeling

Автор: Rissanen J.


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.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

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, $\alpha$-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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