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Tools to improve decision making in an imperfect world
This 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.
Autorentext
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.
Zusammenfassung
Tools to improve decision making in an imperfect world
This 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:
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.
Inhalt
Preface.
1.1 Two Examples.
1.1.1 Public School Class Sizes.
1.1.2 Value at Risk.
1.2 Observables, Unobservables, and Objects of Interest.
1.3 Conditioning and Updating.
1.4 Simulators.
1.5 Modeling.
1.6 Decisionmaking.
2.1 Basics.
2.2 Sufficiency, Ancillarity, and Nuisance Parameters.
2.2.1 Sufficiency.
2.2.2 Ancillarity.
2.2.3 Nuisance Parameters.
2.3 Conjugate Prior Distributions.
2.4 Bayesian Decision Theory and Point Estimation.
2.5 Credible Sets.
2.6 Model Comparison.
2.6.1 Marginal Likelihoods.
2.6.2 Predictive Densities.
3.1 Hierarchical Priors and Latent Variables.
3.2 Improper Prior Distributions.
3.3 Prior Robustness and the Density Ratio Class.
3.4 Asymptotic Analysis.
3.5 The Likelihood Principle.
4.1 Direct Sampling,.
4.2 Acceptance and Importance Sampling.
4.2.1 Acceptance Sampling.
4.2.2 Importance Sampling.
4.3 Markov Chain Monte Carlo.
4.3.1 The Gibbs Sampler.
4.3.2 The Metropolis-Hastings Algorithm.
4.4 Variance Reduction.
4.4.1 Concentrated Expectations.
4.4.2 Antithetic Sampling.
4.5 Some Continuous State Space Markov Chain Theory.
4.5.1 Convergence of the Gibbs Sampler.
4.5.2 Convergence of the Metropolis-Hastings
Algorithm.
4.6 Hybrid Markov Chain Monte Carlo Methods.
4.6.1 Transition Mixtures.
4.6.2 Metropolis within Gibbs.
4.7 Numerical Accuracy and Convergence in Markov Chain Monte
Carlo.
5.1 BACC and the Normal Linear Regression Model.
5.2 Seemingly Unrelated Regressions Models.
5.3 Linear Constraints in the Linear Model.
5.3.1 Linear Inequality Constraints.
5.3.2 Conjectured Linear Restrictions, Linear Inequality
Constraints, and Covariate Selection.
5.4 Nonlinear Regression.
5.4.1 Nonlinear Regression with Smoothness Priors.
5.4.2 Nonlinear Regression with Basis Functions.
6.1 Censored Normal Linear Models.
6.2 Probit Linear Models.
6.3 The Independent Finite State Model.
6.4 Modeling with Mixtures of Normal Distributions.
6.4.1 The Independent Student-t Linear Model.
6.4.2 Normal Mixture Linear Models.
6.4.3 Generalizing the Observable Outcomes.
7.1 Linear Models with Serial Correlation.
7.2 The First-Order Markov Finite State Model.
7.2.1 Inference in the Nonstationary Model.
7.2.2 Inference in the Stationary Model.
7.3 Markov Normal Mixture Linear Model.
8.1 Implementing Simulation Methods.
8.1.1 Density Ratio Tests.
8.1.2 Joint Distribution Tests.
8.2 Formal Model Comparison.
8.2.1 Bayes Factors for Modeling with Common Likelihoods.
8.2.2 Marginal Likelihood Approximation Using Importance
Sampling.
8.2.3 Marginal Likelihood Approximation Using Gibbs
Sampling.
8.2.4 Density Ratio Marginal Likelihood Approximation.
8.3 Model Specification.
8.3.1 Prior Predictive Analysis.
8.3.2 Posterior Predictive Analysis.
8.4 Bayesian Communication.
8.5 Density Ratio Robustness Bounds.
…