## Introduction to Bayesian EconometricsThis book introduces the increasingly popular Bayesian approach to statistics to graduates and advanced undergraduates. In contrast to the long-standing frequentist approach to statistics, the Bayesian approach makes explicit use of prior information and is based on the subjective view of probability. Bayesian econometrics takes probability theory as applying to all situations in which uncertainty exists, including uncertainty over the values of parameters. A distinguishing feature of this book is its emphasis on classical and Markov chain Monte Carlo (MCMC) methods of simulation. The book is concerned with applications of the theory to important models that are used in economics, political science, biostatistics, and other applied fields. These include the linear regression model and extensions to Tobit, probit, and logit models; time series models; and models involving endogenous variables. |

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début page 47

### Contents

Introduction | 3 |

Posterior Distributions and Inference | 20 |

Prior Distributions | 41 |

membership | 50 |

Classical Simulation | 63 |

Basics of Markov Chains | 76 |

Simulation by MCMC Methods | 90 |

U0 1 proposal | 100 |

logit model | 130 |

Multivariate Responses | 134 |

SUR Model | 139 |

Time Series | 153 |

Endogenous Covariates and Sample Selection | 168 |

A Probability Distributions and Matrix Theorems | 182 |

B Computer Programs for MCMC Calculations | 192 |

200 | |

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algorithmic form analyzed aperiodic applied approximate assigned assume assumption autocorrelation Bayes factor Bayesian viewpoint beta distribution binary probit blocks chapter compute conditional distributions conditional posterior distribution conjugate prior consider convergence correlation credibility interval data set defined degrees of freedom denoted density function discussed in Section draw econometrics Equation errors estimate example frequentist gamma distribution Gibbs algorithm Gibbs sampler gth iteration household implies improper prior integral irreducible joint distribution joint posterior distribution kernel large number latent data likelihood function linear regression linear regression model logit model marginal distribution marginal likelihood marginal posterior distributions Markov chain MCMC methods Mean S.D. MH algorithm normal distribution observations oc exp P(st panel data parameters posterior distribution prior distribution probability distribution probit model proposal density random variable response variable simulation specify standard statistical target distribution theorem Tobit truncated unique invariant distribution vector verify wage write zero

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