## Elements of Bayesian StatisticsThe ingratiating title notwithstanding, this is in no standard sense a text but a monograph, based largely upon the authors' research over a period of years, and intended to be read by sophisticated students of theoretical statistics. No exercises attach to the nine chapters, nor are they interrup |

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### Contents

Basic Tools and Notation from Probability Theory | 1 |

ofield | 2 |

Xter Me M Coordinate map | 10 |

Completed subofield 16 69 | 16 |

Sufficiency and Ancillarity | 65 |

Admissible Reductions in Reduced Experiments | 95 |

Maximal Ancillarity | 139 |

Further Results | 187 |

Sequential Experiments | 241 |

Asymptotic Experiments | 283 |

Invariant Experiments | 349 |

463 | |

489 | |

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### Common terms and phrases

admissible analysis ancillary application assumption asymptotic Bayesian experiment called Chapter characterized clearly complete concept conditional expectation conditional independence conditionally consequence consider Corollary defined Definition denoted density distribution dominated equal equivalent exact exactly estimable example exists fact filtration finite function given gives Hence identified implies included interest introduced invariant marginal maximal means measurable measurable separability minimal sufficient mutually sufficient natural Note o-field observations obtain operator parameter parameter space particular posterior predictive presented prior probability problem projection Proof Proposition prove recall reduction regular remark requires respect restriction result sample space sampling sampling theory satisfied Section sense sequence sequential shift shows specification splitting strong structure sub-o-field sufficient parameter sufficient statistic surely Theorem tion transformations transitivity trivial true