# MCMC

[Robert and Casella (2013)](https://www.springer.com/gp/book/9781475730715) provides the following definition:

![](https://666993855-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2F-LJfsESZOIJn_3uGIecs%2F-LKQ4DYZY7f2lR8zQLF4%2F-LKQ4E6e7uZCupe01zdH%2Fmcmc-def.png?generation=1534831425610289\&alt=media)

For illustration, you can visit the jupyter notebook on [MCMC\_example](http://nbviewer.jupyter.org/github/szcf-weiya/MonteCarlo/blob/master/MCMC/MCMC_example.ipynb)

Working principle: For an arbitrary starting value $$x^{(0)}$$, a chain $$X^{(t)}$$ is generated using a transition kernel with stationary distribution $$f$$, which ensures the convergence in distribution of $$X^{(t)}$$ to a random variable from $$f$$.

Some good materials about MCMC.

1. <https://cosx.org/2013/01/lda-math-mcmc-and-gibbs-sampling>