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Autor: John Geweke
ISBN-13: 9780471744726
Einband: E-Book
Seiten: 300
Sprache: Englisch
eBook Typ: PDF
eBook Format: E-Book
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Contemporary Bayesian Econometrics and Statistics

Wiley Series in Probability and Statistics
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1
Tools to improve decision making in an imperfect world
This publication provides readers with a thorough understanding ofBayesian analysis that is grounded in the theory of inference andoptimal decision making. Contemporary Bayesian Econometrics andStatistics provides readers with state-of-the-art simulationmethods and models that are used to solve complex real-worldproblems. Armed with a strong foundation in both theory andpractical problem-solving tools, readers discover how to optimizedecision making when faced with problems that involve limited orimperfect data.

The book begins by examining the theoretical and mathematicalfoundations of Bayesian statistics to help readers understand howand why it is used in problem solving. The author then describeshow modern simulation methods make Bayesian approaches practicalusing widely available mathematical applications software. Inaddition, the author details how models can be applied to specificproblems, 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 decadeof classroom experience, and readers will find the author'sapproach very engaging and accessible. There are nearly 200examples and exercises to help readers see how effective use ofBayesian statistics enables them to make optimal decisions. MATLAB?and R computer programs are integrated throughout the book. Anaccompanying Web site provides readers with computer code for manyexamples and datasets.

This publication is tailored for research professionals who useeconometrics and similar statistical methods in their work. Withits emphasis on practical problem solving and extensive use ofexamples and exercises, this is also an excellent textbook forgraduate-level students in a broad range of fields, includingeconomics, statistics, the social sciences, business, and publicpolicy.
4
Preface.

1. Introduction.

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. Elements of Bayesian Inference.

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. Topics in Bayesian Inference.

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. Posterior Simulation.

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-HastingsAlgorithm.

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 MonteCarlo.

5. Linear Models.

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 InequalityConstraints, and Covariate Selection.

5.4 Nonlinear Regression.

5.4.1 Nonlinear Regression with Smoothness Priors.

5.4.2 Nonlinear Regression with Basis Functions.

6. Modeling with Latent Variables.

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. Modeling for Time Series.

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. Bayesian Investigation.

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 ImportanceSampling.

8.2.3 Marginal Likelihood Approximation Using GibbsSampling.

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.

Bibliography.

Author Index.

Subject Index.

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Autor: John Geweke
ISBN-13 :: 9780471744726
ISBN: 0471744727
Verlag: John Wiley & Sons
Seiten: 300
Sprache: Englisch
Auflage 1. Auflage
Sonstiges: Ebook