臺灣博碩士論文加值系統

Markov chain Monte Carlo (MCMC) methods are extremely popular tools
in econometrics. Both of Bayesians and frequentists may find this method
useful. We review the Bayesian foundation for deriving the posterior condi-tionals.
Then we discuss several sampling algorithms, especially in Metropolis—
Hastings algorithm and Gibbs sampling algorithm, and properties of the Markov
chain. For constructing a complete concept of MCMC method, we use several
important econometric models to illustrate the implementing of the MCMC
method. We discuss also the implementing issue on sampling from a specified
distribution, the dependency between the drawing samples and choosing the
number of burn-in.

Markov chain Monte Carlo (MCMC) methods are extremely popular tools
in econometrics. Both of Bayesians and frequentists may find this method
useful. We review the Bayesian foundation for deriving the posterior condi-tionals.
Then we discuss several sampling algorithms, especially in Metropolis—
Hastings algorithm and Gibbs sampling algorithm, and properties of the Markov
chain. For constructing a complete concept of MCMC method, we use several
important econometric models to illustrate the implementing of the MCMC
method. We discuss also the implementing issue on sampling from a specified
distribution, the dependency between the drawing samples and choosing the
number of burn-in.

1 Introduction 1
2 Bayesian Foundation 4
2.1 Classical Linear Regression Model with Known ˙ 2 . . . . . . . . 5
2.2 Classical Linear Regression Model with Unknown ˙ 2 . . . . . . 7
2.3 Linear Regression Model with Known . . . . . . . . . . . . . 8
3 Markov Chain Monte Carlo 12
3.1 The Inverse Transform Method . . . . . . . . . . . . . . . . . . 12
3.2 The Acceptance—Rejection Method . . . . . . . . . . . . . . . . 14
3.3 Markov Chain Monte Carlo Method . . . . . . . . . . . . . . . . 17
3.3.1 Markov Chain . . . . . . . . . . . . . . . . . . . . . . . . 18
3.4 Metropolis-Hastings Algorithm . . . . . . . . . . . . . . . . . . 21
3.5 Gibbs Sampling Algorithm . . . . . . . . . . . . . . . . . . . . . 23
4 Applications 25
4.1 Unobserved or Missing Data . . . . . . . . . . . . . . . . . . . . 26
4.2 Nuisance Parameters . . . . . . . . . . . . . . . . . . . . . . . . 32
4.3 Tips for Implementing . . . . . . . . . . . . . . . . . . . . . . . 34
4.3.1 Multivariate Normal . . . . . . . . . . . . . . . . . . . . 34
4.3.2 Inverse Gamma . . . . . . . . . . . . . . . . . . . . . . . 34
4.3.3 Truncated Normal . . . . . . . . . . . . . . . . . . . . . 35
4.3.4 How to Choose the number of burn-in no . . . . . . . . . 36
5 Conclusions and Suggestions 37
References 36

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