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```Contents
List of Figures page ix
List of Tables xi
Preface xiii
Part I Fundamentals of Bayesian Inference
1 Introduction 3
1.1 Econometrics 3
1.2 Plan of the Book 4
1.3 Historical Note and Further Reading 5
2 Basic Concepts of Probability and Inference 7
2.1 Probability 7
2.1.1 Frequentist Probabilities 8
2.1.2 Subjective Probabilities 9
2.2 Prior, Likelihood, and Posterior 12
2.3 Summary 18
2.4 Further Reading and References 19
2.5 Exercises 19
3 Posterior Distributions and Inference 20
3.1 Properties of Posterior Distributions 20
3.1.1 The Likelihood Function 20
3.1.2 Vectors of Parameters 22
3.1.3 Bayesian Updating 24
3.1.4 Large Samples 25
3.1.5 Identification 28
3.2 Inference 29
3.2.1 Point Estimates 29
3.2.2 Interval Estimates 31
3.2.3 Prediction 32
3.2.4 Model Comparison 33
3.3 Summary 38
3.4 Further Reading and References 38
3.5 Exercises 39
4 Prior Distributions 41
4.1 Normal Linear Regression Model 41
4.2 Proper and Improper Priors 43
4.3 Conjugate Priors 44
4.4 Subject-Matter Considerations 47
4.5 Exchangeability 50
4.6 Hierarchical Models 52
4.7 Training Sample Priors 53
4.8 Sensitivity and Robustness 54
4.9 Conditionally Conjugate Priors 54
4.11 Further Reading and References 57
4.12 Exercises 58
Part II Simulation
5 Classical Simulation 63
5.1 Probability Integral Transformation Method 63
5.2 Method of Composition 65
5.3 Accept¿Reject Algorithm 66
5.4 Importance Sampling 70
5.5 Multivariate Simulation 72
5.6 Using Simulated Output 72
5.7 Further Reading and References 74
5.8 Exercises 75
6 Basics of Markov Chains 76
6.1 Finite State Spaces 76
6.2 Countable State Spaces 81
6.3 Continuous State Spaces 85
6.4 Further Reading and References 87
6.5 Exercises 87
7 Simulation by MCMC Methods 90
7.1 Gibbs Algorithm 91
7.1.1 Basic Algorithm 91
7.1.2 Calculation of Marginal Likelihood 95
7.2 Metropolis¿Hastings Algorithm 96
7.2.1 Basic Algorithm 96
7.2.2 Calculation of Marginal Likelihood 101
7.3 Numerical Standard Errors and Convergence 102
7.4 Further Reading and References 103
7.5 Exercises 105
Part III Applications
8 Linear Regression and Extensions 111
8.1 Continuous Dependent Variables 111
8.1.1 Normally Distributed Errors 111
8.1.2 Student-t Distributed Errors 114
8.2 Limited Dependent Variables 117
8.2.1 Tobit Model for Censored Data 117
8.2.2 Binary Probit Model 122
8.2.3 Binary Logit Model 126
8.3 Further Reading and References 129
8.4 Exercises 132
9 Multivariate Responses 134
9.1 SUR Model 134
9.2 Multivariate Probit Model 139
9.3 Panel Data 144
9.4 Further Reading and References 149
9.5 Exercises 151
10 Time Series 153
10.1 Autoregressive Models 153
10.2 Regime-Switching Models 158
10.3 Time-Varying Parameters 161
10.4 Time Series Properties of Models for Panel Data 165
10.5 Further Reading and References 166
10.6 Exercises 167
11 Endogenous Covariates and Sample Selection 168
11.1 Treatment Models 168
11.2 Endogenous Covariates 173
11.3 Incidental Truncation 175
11.4 Further Reading and References 179
11.5 Exercises 180
A Probability Distributions and Matrix Theorems 182
A.1 Probability Distributions 182
A.1.1 Bernoulli 182
A.1.2 Binomial 182
A.1.3 Negative Binomial 183
A.1.4 Multinomial 183
A.1.5 Poisson 183
A.1.6 Uniform 183
A.1.7 Gamma 184
A.1.8 Inverted or Inverse Gamma 184
A.1.9 Beta 185
A.1.10 Dirichlet 185
A.1.11 Normal or Gaussian 186
A.1.12 Multivariate and Matricvariate Normal or Gaussian 186
A.1.13 Truncated Normal 188
A.1.14 Univariate Student-t 188
A.1.15 Multivariate t 188
A.1.16 Wishart 190
A.1.17 Inverted or Inverse Wishart 190
A.1.18 Multiplication Rule of Probability 190
A.2 Matrix Theorems 191
B Computer Programs for MCMC Calculations 192¿193
Bibliography 194
Author Index 200
Subject Index 202¿204
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Library of Congress Subject Headings for this publication:

Econometrics.
Bayesian statistical decision theory.