## Maximum-Entropy and Bayesian Methods in Science and Engineering: FoundationsThis volume has its origin in the Fifth, Sixth and Seventh Workshops on and Bayesian Methods in Applied Statistics", held at "Maximum-Entropy the University of Wyoming, August 5-8, 1985, and at Seattle University, August 5-8, 1986, and August 4-7, 1987. It was anticipated that the proceedings of these workshops would be combined, so most of the papers were not collected until after the seventh workshop. Because all of the papers in this volume are on foundations, it is believed that the con tents of this volume will be of lasting interest to the Bayesian community. The workshop was organized to bring together researchers from different fields to critically examine maximum-entropy and Bayesian methods in science and engineering as well as other disciplines. Some of the papers were chosen specifically to kindle interest in new areas that may offer new tools or insight to the reader or to stimulate work on pressing problems that appear to be ideally suited to the maximum-entropy or Bayesian method. A few papers presented at the workshops are not included in these proceedings, but a number of additional papers not presented at the workshop are included. In particular, we are delighted to make available Professor E. T. Jaynes' unpublished Stanford University Microwave Laboratory Report No. 421 "How Does the Brain Do Plausible Reasoning?" (dated August 1957). This is a beautiful, detailed tutorial on the Cox-Polya-Jaynes approach to Bayesian probability theory and the maximum-entropy principle. |

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### Contents

How Does the Brain Do Plausible Reasoning? | 1 |

THE RELATION OF BAYESIAN AND MAXIMUM ENTROPY METHODS | 25 |

AN ENGINEER LOOKS AT BAYES | 31 |

BAYESIAN INDUCTIVE INFERENCE AND MAXIMUM ENTROPY | 53 |

Excerpts from Bayesian Spectrum Analysis and Parameter Estimation | 75 |

DETECTION OF EXTRASOLAR SYSTEM PLANETS | 147 |

STOCHASTIC COMPLEXITY AND THE MAXIMUM ENTROPY PRINCIPLE | 161 |

THE AXIOMS OF MAXIMUM ENTROPY | 173 |

Quantum Density Matrix and Entropic Uncertainty | 235 |

INFORMATIONTHEORETICAL GENERALIZATION OF THE UNCERTAINTY PRINCIPLE | 245 |

TIME ENERGY AND THE LIMITS OF MEASUREMENT | 249 |

ON A DETECTION ESTIMATOR RELATED TO ENTROPY | 257 |

THE EVOLUTION OF CARNOTS PRINCIPLE | 267 |

A LOGIC OF INFORMATION SYSTEMS | 283 |

METHODOLOGICAL PRINCIPLES OF UNCERTAINTY IN INDUCTIVE MODELLING | 295 |

COMPARISON OF MINIMUM CROSSENTROPY INFERENCE WITH MINIMALLY INFORMATIVE INFORMATION SYSTEMS | 305 |

UNDERSTANDING IGNORANCE | 189 |

MAXIMUM ENTROPY CALCULATIONS ON A DISCRETE PROBABILITY SPACE | 205 |

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