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Conditional Moment Restrictions" Journal
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Chapter 45 in Handbook of Econometrics
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An Introduction to Modern Bayesian Econometrics
Source: www.econ.brown.edu
Topic: Econometrics
Sort Desciption: This book is an introduction to the Bayesian approach to econometrics. ... Bayesian econometrics and this is a radically different approach to our subject ...
Content Inside: An Introduction to Modern Bayesian Econometrics Tony Lancaster May 26 2003 ii Contents Introduction xi 1 The Bayesian Algorithm 1 1.1 Econometric Analysis 1 1.2 Statistical Analysis 2 1.3 Bayes Theorem 3 1.3.1 Parameters and Data 8 1.3.2 The Bayesian Algorithm . 9 1.4 The Components of Bayes Theorem 9 1.4.1 The Likelihood p(y|) 10 1.4.2 The Prior p() 28 1.4.3 The Posterior p(|y) . 39 1.5 Conclusion and Summary 56 1.6 Exercises and Complements . 57 1.7 Appendix to Chapter 1: Some Probability Distributions . 63 1.8 Bibliographic Notes 66 2 Prediction and Model Criticism 69 2.1 Methods of Model Checking . 70 2.2 Informal Model Checks 71 2.2.1 Residual QQ Plots 72 2.3 Uncheckable Beliefs? . 76 2.4 Formal Model Checks 79 2.4.1 Predictive Distributions . 79 2.4.2 The Prior Predictive Distribution 79 2.4.3 Using the Prior Predictive Distribution to Check your Model 81 2.4.4 Improper Prior Predictive Distributions 83 2.4.5 Prediction from Training Samples . 84 2.5 Posterior Prediction . 87 2.5.1 Posterior Model Checking 89 2.5.2 Sampling the Predictive Distribution 90 2.6 Posterior Odds and Model Choice . 97 2.6.1 Two Approximations to Bayes Factors . 99 iii iv CONTENTS 2.7 Enlarging the Model . 100 2.8 Summary . 105 2.9 Exercises and Further Examples 106 2.10 Bibliographic Notes 110 3 Linear Regression Models 113 3.1 Introduction 113 3.2 Economists and Regression Models 113 3.2.1 Mean Independence . 115 3.3 Linear Regression Models 115 3.3.1 Independent Normal Homoscedastic Errors 117 3.3.2 Vague Prior Beliefs about and 120 3.3.3 The Two Marginals under a Vague Prior 121 3.3.4 Highest Posterior Density Intervals and Regions . 128 3.3.5 The Least Squares Line . 131 3.3.6 Informative Prior Beliefs . 134 3.3.7 Sampling the posterior density of . 135 3.3.8 An Approximate Joint Posterior Distribution . 136 3.4 A Multinomial Approach to Linear Regression 143 3.4.1 Comments on the Mul ...
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