Screen LibraryStochastic complexity in statistical inquiry /
This book describes how model selection and statistical inference can be founded on the shortest code length for the observed data, called the stochastic complexity. This generalization of the algorithmic complexity not only offers an objective view of statistics, where no prejudiced assumptions of...
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| Main Authors: | |
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| Corporate Authors: | |
| Published: |
World Scientific Pub. Co.,
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| Publisher Address: | Singapore ; River Edge, N.J. : |
| Publication Dates: | 1989. |
| Literature type: | eBook |
| Language: | English |
| Subjects: | |
| Online Access: |
http://www.worldscientific.com/worldscibooks/10.1142/0822#t=toc |
| Summary: |
This book describes how model selection and statistical inference can be founded on the shortest code length for the observed data, called the stochastic complexity. This generalization of the algorithmic complexity not only offers an objective view of statistics, where no prejudiced assumptions of "true" data generating distributions are needed, but it also in one stroke leads to calculable expressions in a range of situations of practical interest and links very closely with mainstream statistical theory. The search for the smallest stochastic complexity extends the classical maximum likelihood technique to a new global one, in which models can be compared regardless of their numbers of parameters. The result is a natural and far reaching extension of the traditional theory of estimation, where the Fisher information is replaced by the stochastic complexity and the Cramer-Rao inequality by an extension of the Shannon-Kullback inequality. Ideas are illustrated with applications from parametric and non-parametric regression, density and spectrum estimation, time series, hypothesis testing, contingency tables, and data compression. |
| Carrier Form: | 1 online resource (x,177pages) : illustrations |
| Bibliography: | Includes bibliographical references and index. |
| ISBN: | 9789812385499 |
| Index Number: | QA267 |
| CLC: | O211.6 |
| Contents: | 1. Introduction -- 2. Models, codes, and complexity. 2.1. Models of data. 2.2. Coding. 2.3. Shannon complexity. 2.4. Combinatorial complexity. 2.5 Algorithmic complexity. 2.6. Complexity in a coding system -- 3. Stochastic complexity. 3.1. Two-part codes. 3.2. Stochastic complexity. 3.3. Predictive coding. 3.4. Main inequality. 3.5. Non-parametric model classes. 3.6. The MDL principle. 3.7. Alternative approaches -- 4. Model validation. 4.1. Confidence in parameter estimates. 4.2. Hypothesis testing -- 5. Linear regression. 5.1. The least squares principle. 5.2. Single-variate selection-of-variables problem. 5.3. Multi-variate selection-of-variables problem. 5.4. Properties of PLS estimates -- 6. Time series. 6.1. Prediction of ARMA processes. 6.2 ARMA estimation -- 7. Applications. 7.1. Classification. 7.2. Tree classifiers. 7.3. Algorithm context. |