## Bayesian Statistics: An IntroductionBayesian Statistics is the school of thought that combines prior beliefs with the likelihood of a hypothesis to arrive at posterior beliefs. The first edition of Peter Lee’s book appeared in 1989, but the subject has moved ever onwards, with increasing emphasis on Monte Carlo based techniques. This new fourth edition looks at recent techniques such as variational methods, Bayesian importance sampling, approximate Bayesian computation and Reversible Jump Markov Chain Monte Carlo (RJMCMC), providing a concise account of the way in which the Bayesian approach to statistics develops as well as how it contrasts with the conventional approach. The theory is built up step by step, and important notions such as sufficiency are brought out of a discussion of the salient features of specific examples.
- Includes expanded coverage of Gibbs sampling, including more numerical examples and treatments of OpenBUGS, R2WinBUGS and R2OpenBUGS.
- Presents significant new material on recent techniques such as Bayesian importance sampling, variational Bayes, Approximate Bayesian Computation (ABC) and Reversible Jump Markov Chain Monte Carlo (RJMCMC).
- Provides extensive examples throughout the book to complement the theory presented.
- Accompanied by a supporting website featuring new material and solutions.
More and more students are realizing that they need to learn Bayesian statistics to meet their academic and professional goals. This book is best suited for use as a main text in courses on Bayesian statistics for third and fourth year undergraduates and postgraduate students. |

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### Contents

Bayesian inference for the normal distribution | |

Hypothesis testing 4 1 Hypothesis testing 4 2 Onesided hypothesis tests 4 3 Lindleys method 4 4 Point or sharpnull hypotheses with prior information | |

Twosample problems | |

variance | |

3Regression andthebivariate normalmodel 6 4Conjugate | |

Othertopics 7 1 The likelihoodprinciple 7 2 The stopping rule principle | |

methods | |

2TheEM algorithm 9 3Data augmentation by Monte Carlo 9 4TheGibbs sampler | |

Some approximate methods | |

Common statistical distributions | |