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From Statistical Physics to Statistical Inference and Back / Edition 1

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Overview

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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Product Details

  • ISBN-13: 9780792327752
  • Publisher: Springer Netherlands
  • Publication date: 3/31/1994
  • Series: Nato Science Series C: (closed) , #428
  • Edition description: 1994
  • Edition number: 1
  • Pages: 355
  • Product dimensions: 9.21 (w) x 6.14 (h) x 0.81 (d)

Table of Contents

Preface
Remarks 1
Statistical mechanics and the maximum entropy method 11
Irreversibility, probability and entropy 45
Maximum entropy for random cellular structures 77
Minimal Description Length modeling: an introduction 95
An introduction to learning and generalization 105
Information geometry and manifolds of neural networks 113
Uncertainty as a resource for managing complexity 139
The development of Information Theory 155
Statistical inference, zero-knowledge and proofs of identity 169
Spin glasses: an introduction 183
Statistical Mechanics and error-correcting codes 195
Learning and generalization with undetermined architecture 205
Confronting neural network and human behavior in a quasiregular environment 225
Sensory processing and information theory 237
The formation of representations in the visual cortex 249
Classifier systems: models for learning agents 263
Space time dynamics and biorthogonal analysis: mementum 281
Symbolic encoding in dynamical systems 293
Topological organization of (low-dimensional) chaos 311
Noise Separation and MDL modeling of chaotic processes 317
Inference in Quantum Mechanics 331
Decoherence and the existential interpretation of quantum theory or "no information without representation" 341
List of Contributors 351
Index 353
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