TY  - JOUR
TI  - On Markov Chain Monte Carlo Methods
T2  - HSE Economic Journal 
IS  - HSE Economic Journal 
KW  - multivariate density simulation
KW  - Metropolis algorithm
KW  - Gibbs sampling
AB  - This paper examines two Markov chain Monte Carlo methods that have been widely used in econometrics. An introductory exposition of the Metropolis algorithm and the Gibbs sampler is provided. These methods are used to simulate multivariate distributions. Many problems in Bayesian statistics can be solved by simulating the posterior distribution. Invariance condition is of importance, the proofs are given for both meth ods. We use finite Markov chains to explore and substantiate the methods. Several examples are provided to illustrate the applicability and efficiency of the Markov chain Monte Carlo methods. They include bivariate normal distribution with high correlation, bivaria­te exponential distribution, mixture of bivariate normals.
AU  - Alexey Shvedov
UR  - https://ej.hse.ru/en/2010-14-2/26550023.html
PY  - 2010
SP  - 227-243
VL  - 14