Ebook: From Statistical Physics to Statistical Inference and Back

Physicists, when modelling physical systems with a large number of degrees of freedom, and statisticians, when performing data analysis, have developed their own concepts and methods for making the `best' inference. But are these methods equivalent, or not? What is the state of the art in making inferences? The physicists want answers. More: neural computation demands a clearer understanding of how neural systems make inferences; the theory of chaotic nonlinear systems as applied to time series analysis could profit from the experience already booked by the statisticians; and finally, there is a long-standing conjecture that some of the puzzles of quantum mechanics are due to our incomplete understanding of how we make inferences. Matter enough to stimulate the writing of such a book as the present one.
But other considerations also arise, such as the maximum entropy method and Bayesian inference, information theory and the minimum description length. Finally, it is pointed out that an understanding of human inference may require input from psychologists. This lively debate, which is of acute current interest, is well summarized in the present work.

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Content:
Front Matter....Pages i-viii
Concluding Remarks....Pages 1-9
Statistical Mechanics and the Maximum Entropy Method....Pages 11-43
Irreversibility, Probability and Entropy....Pages 45-75
Maximum Entropy for Random Cellular Structures....Pages 77-93
MDL Modeling — An Introduction....Pages 95-104
An Introduction to Learning and Generalisation....Pages 105-112
Information Geometry and Manifolds of Neural Networks....Pages 113-138
Uncertainty as a Resource for Managing Complexity....Pages 139-153
The Development of Information Theory....Pages 155-167
Statistical Inference, Zero Knowledge and Proofs of Identity....Pages 169-182
Spin Glasses: An Introduction....Pages 183-193
Statistical Mechanics and Error-Correcting Codes....Pages 195-204
Learning and Generalization with Undetermined Architecture....Pages 205-224
Confronting Neural Network and Human Behavior in a Quasiregular Environment....Pages 225-235
Sensory Processing and Information Theory....Pages 237-247
The Formation of Representations in the Visual Cortex....Pages 249-261
Classifier Systems: Models for Learning Agents....Pages 263-280
Space Time Dynamics and Biorthogonal Analysis Mementum....Pages 281-291
Symbolic Encoding in Dynamical Systems....Pages 293-309
Topological Organization of (Low-Dimensional) Chaos....Pages 311-316
Noise Separation and MDL Modeling of Chaotic Processes....Pages 317-330
Inference in Quantum Mechanics....Pages 331-339
Decoherence and the Existential Interpretation of Quantum Theory, or ”No Information Without Representation”....Pages 341-350
Back Matter....Pages 351-355

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Content:
Front Matter....Pages i-viii
Concluding Remarks....Pages 1-9
Statistical Mechanics and the Maximum Entropy Method....Pages 11-43
Irreversibility, Probability and Entropy....Pages 45-75
Maximum Entropy for Random Cellular Structures....Pages 77-93
MDL Modeling — An Introduction....Pages 95-104
An Introduction to Learning and Generalisation....Pages 105-112
Information Geometry and Manifolds of Neural Networks....Pages 113-138
Uncertainty as a Resource for Managing Complexity....Pages 139-153
The Development of Information Theory....Pages 155-167
Statistical Inference, Zero Knowledge and Proofs of Identity....Pages 169-182
Spin Glasses: An Introduction....Pages 183-193
Statistical Mechanics and Error-Correcting Codes....Pages 195-204
Learning and Generalization with Undetermined Architecture....Pages 205-224
Confronting Neural Network and Human Behavior in a Quasiregular Environment....Pages 225-235
Sensory Processing and Information Theory....Pages 237-247
The Formation of Representations in the Visual Cortex....Pages 249-261
Classifier Systems: Models for Learning Agents....Pages 263-280
Space Time Dynamics and Biorthogonal Analysis Mementum....Pages 281-291
Symbolic Encoding in Dynamical Systems....Pages 293-309
Topological Organization of (Low-Dimensional) Chaos....Pages 311-316
Noise Separation and MDL Modeling of Chaotic Processes....Pages 317-330
Inference in Quantum Mechanics....Pages 331-339
Decoherence and the Existential Interpretation of Quantum Theory, or ”No Information Without Representation”....Pages 341-350
Back Matter....Pages 351-355
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