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Introduction to Bayesian Econometrics: A GUIded tour using R
Introduction
Preface
To instructors and students
Acknowledgments
1
Basic formal concepts
1.1
The Bayes’ rule
1.2
Bayesian framework: A brief summary of theory
1.3
Bayesian reports: Decision theory under uncertainty
1.4
Summary
1.5
Exercises
2
Conceptual differences between the Bayesian and Frequentist approaches
2.1
The concept of probability
2.2
Subjectivity is not the key
2.3
Estimation, hypothesis testing and prediction
2.4
The likelihood principle
2.5
Why is not the Bayesian approach that popular?
2.6
A simple working example
2.7
Summary
2.8
Exercises
3
Cornerstone models: Conjugate families
3.1
Motivation of conjugate families
3.1.1
Examples of exponential family distributions
3.2
Conjugate prior to exponential family
3.2.1
Examples: Theorem 4.2.1
3.3
Linear regression: The conjugate normal-normal/inverse gamma model
3.4
Multivariate linear regression: The conjugate normal-normal/inverse Wishart model
3.5
Summary
3.6
Exercises
4
Simulation methods
4.1
Markov Chain Monte Carlo methods
4.1.1
Gibbs sampler
4.1.2
Metropolis-Hastings
4.1.3
Hamiltonian Monte Carlo
4.2
Importance sampling
4.3
Particle filtering
4.4
Convergence diagnostics
4.4.1
Numerical standard error
4.4.2
Effective number of simulation draws
4.4.3
Tests of convergence
4.4.4
Checking for errors in the posterior simulator
4.5
Summary
4.6
Exercises
5
Graphical user interface
5.1
Introduction
5.2
Univariate models
5.3
Multivariate models
5.4
Time series models
5.5
Longitudinal/panel models
5.6
Bayesian model average
5.7
Help
5.8
Warning
6
Univariate regression
6.1
The Gaussian linear model
6.2
The logit model
6.3
The probit model
6.4
The multinomial probit model
6.5
The multinomial logit model
6.6
Ordered probit model
6.7
Negative binomial model
6.8
Tobit model
6.9
Quantile regression
6.10
Bayesian bootstrap regression
6.11
Summary
6.12
Exercises
7
Multivariate regression
7.1
Multivariate regression
7.2
Seemingly Unrelated Regression
7.3
Instrumental variable
7.4
Multivariate probit model
7.5
Summary
7.6
Exercises
8
Time series
8.1
State-space representation
8.1.1
Gaussian linear state-space models
8.2
ARMA processes
8.3
Stochastic volatility models
8.4
Vector Autoregressive models
8.5
Summary
8.6
Exercises
9
Longitudinal regression
9.1
Normal model
9.2
Logit model
9.3
Poisson model
9.4
Summary
9.5
Exercises
10
Bayesian model averaging in variable selection
10.1
Foundation
10.2
The Gaussian linear model
10.3
Generalized linear models
10.4
Calculating the marginal likelihood
10.4.1
Savage-Dickey density ratio
10.4.2
Chib’s methods
10.4.3
Gelfand-Dey method
10.5
Summary
10.6
Exercises
11
Semi-parametric and non-parametric models
11.1
Mixture models
11.1.1
Finite Gaussian mixtures
11.1.2
Dirichlet processes
11.2
Non-parametric generalized additive models
12
Machine learning
12.1
Cross validation and Bayes factors
12.2
Regularization
12.2.1
Bayesian LASSO
12.2.2
Stochastic search variable selection
12.2.3
Non-local priors
12.3
Bayesian additive regression trees
12.4
Gaussian processes
13
Causal inference
13.1
Instrumental variables
13.1.1
Semi-parametric IV model
13.2
Regression discontinuity design
13.3
Regression kink design
13.4
Synthetic control
13.5
Difference in difference estimation
13.6
Event Analysis
13.7
Bayesian exponential tilted empirical likelihood
13.8
Double-Debiased machine learning causal effects
14
Approximation methods
14.1
Approximate Bayesian computation
14.2
Bayesian synthetic likelihood
14.3
Expectation propagation
14.4
Integrated nested Laplace approximations
14.5
Variational Bayes
Appendix
References
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Introduction to Bayesian Data Modeling
Chapter 14
Approximation methods