Contemporary Bayesian Econometrics And Statistics

by Geweke, John

• ISBN13: 9780471679325
• ISBN10: 0471679321
• Edition: 1st
• Format: Hardcover
• Copyright: 2005-09-14
• Publisher: Wiley-Interscience

Summary

Tools to improve decision making in an imperfect worldThis publication provides readers with a thorough understanding of Bayesian analysis that is grounded in the theory of inference and optimal decision making. Contemporary Bayesian Econometrics and Statistics provides readers with state-of-the-art simulation methods and models that are used to solve complex real-world problems. Armed with a strong foundation in both theory and practical problem-solving tools, readers discover how to optimize decision making when faced with problems that involve limited or imperfect data.The book begins by examining the theoretical and mathematical foundations of Bayesian statistics to help readers understand how and why it is used in problem solving. The author then describes how modern simulation methods make Bayesian approaches practical using widely available mathematical applications software. In addition, the author details how models can be applied to specific problems, including: Linear models and policy choices Modeling with latent variables and missing data Time series models and prediction Comparison and evaluation of models The publication has been developed and fine- tuned through a decade of classroom experience, and readers will find the author's approach very engaging and accessible. There are nearly 200 examples and exercises to help readers see how effective use of Bayesian statistics enables them to make optimal decisions. MATLAB? and R computer programs are integrated throughout the book. An accompanying Web site provides readers with computer code for many examples and datasets.This publication is tailored for research professionals who use econometrics and similar statistical methods in their work. With its emphasis on practical problem solving and extensive use of examples and exercises, this is also an excellent textbook for graduate-level students in a broad range of fields, including economics, statistics, the social sciences, business, and public policy.

Author Biography

JOHN GEWEKE, PHD, is Harlan McGregor Chair in Economic Theory and Professor of Economics and Statistics at the University of Iowa. He is an elected Fellow of the Econometric Society and the American Statistical Association, former President of the International Society for Bayesian Analysis, and coeditor of the Journal of Econometrics.

Table of Contents

Preface	ix
Introduction	1	(20)
Two Examples	3	(4)
Public School Class Sizes	4	(1)
Value at Risk	5	(2)
Observables, Unobservables, and Objects of Interest	7	(3)
Conditioning and Updating	10	(3)
Simulators	13	(2)
Modeling	15	(2)
Decisionmaking	17	(4)
Elements of Bayesian Inference	21	(52)
Basics	21	(10)
Sufficiency, Ancillarity, and Nuisance Parameters	31	(7)
Sufficiency	31	(2)
Ancillarity	33	(2)
Nuisance Parameters	35	(3)
Conjugate Prior Distributions	38	(8)
Bayesian Decision Theory and Point Estimation	46	(10)
Credible Sets	56	(5)
Model Comparison	61	(12)
Marginal Likelihoods	62	(4)
Predictive Densities	66	(7)
Topics in Bayesian Inference	73	(32)
Hierarchical Priors and Latent Variables	73	(5)
Improper Prior Distributions	78	(9)
Prior Robustness and the Density Ratio Class	87	(4)
Asymptotic Analysis	91	(6)
The Likelihood Principle	97	(8)
Posterior Simulation	105	(48)
Direct Sampling	106	(4)
Acceptance and Importance Sampling	110	(9)
Acceptance Sampling	111	(3)
Importance Sampling	114	(5)
Markov Chain Monte Carlo	119	(8)
The Gibbs Sampler	120	(2)
The Metropolis--Hastings Algorithm	122	(5)
Variance Reduction	127	(6)
Concentrated Expectations	128	(2)
Antithetic Sampling	130	(3)
Some Continuous State Space Markov Chain Theory	133	(9)
Convergence of the Gibbs Sampler	137	(2)
Convergence of the Metropolis--Hastings Algorithm	139	(3)
Hybrid Markov Chain Monte Carlo Methods	142	(3)
Transition Mixtures	142	(1)
Metropolis within Gibbs	143	(2)
Numerical Accuracy and Convergence in Markov Chain Monte Carlo	145	(8)
Linear Models	153	(42)
BACC and the Normal Linear Regression Model	154	(8)
Seemingly Unrelated Regressions Models	162	(7)
Linear Constraints in the Linear Model	169	(6)
Linear Inequality Constraints	170	(2)
Conjectured Linear Restrictions, Linear Inequality Constraints, and Covariate Selection	172	(3)
Nonlinear Regression	175	(20)
Nonlinear Regression with Smoothness Priors	176	(9)
Nonlinear Regression with Basis Functions	185	(10)
Modeling with Latent Variables	195	(26)
Censored Normal Linear Models	196	(4)
Probit Linear Models	200	(2)
The Independent Finite State Model	202	(3)
Modeling with Mixtures of Normal Distributions	205	(16)
The Independent Student-t Linear Model	206	(2)
Normal Mixture Linear Models	208	(7)
Generalizing the Observable Outcomes	215	(6)
Modeling for Time Series	221	(24)
Linear Models with Serial Correlation	222	(4)
The First-Order Markov Finite State Model	226	(7)
Inference in the Nonstationary Model	229	(1)
Inference in the Stationary Model	230	(3)
Markov Normal Mixture Linear Model	233	(12)
Bayesian Investigation	245	(38)
Implementing Simulation Methods	246	(9)
Density Ratio Tests	247	(4)
Joint Distribution Tests	251	(4)
Formal Model Comparison	255	(7)
Bayes Factors for Modeling with Common Likelihoods	255	(1)
Marginal Likelihood Approximation Using Importance Sampling	256	(1)
Marginal Likelihood Approximation Using Gibbs Sampling	257	(2)
Density Ratio Marginal Likelihood Approximation	259	(3)
Model Specification	262	(9)
Prior Predictive Analysis	262	(5)
Posterior Predictive Analysis	267	(4)
Bayesian Communication	271	(6)
Density Ratio Robustness Bounds	277	(6)
Bibliography	283	(10)
Author Index	293	(2)
Subject Index	295