## Archive for the ‘Markov Chains’ Category

### Handbook of Markov Chain Monte Carlo

Today I received my copy of “Handbook of Markov Chain Monte Carlo“. Up to now I have consulted “Monte Carlo Strategies in Scientific Computing” of Jun S.Liu. In this post I will give my first thought on the new book.

The book of Liu is indeed awesome. The author himself has made many original contributions to sampling algorithms, and many of his ideas was explained in the book. The chapters on Gibbs Sampler (chapter 6),General Conditional Sampling (chapter 7) and multi-chain MCMC (chapter 10, 11) were excellent. But given that the book was written 10 years ago, many recent developments is missing. Some algorithms were not given enough spaces (in particular, Reversible Jump MCMC was given only  2 pages!).

Exercise 7.12: Let $X_{n}$ be the sum of $n$ independent rolls of a fair dice. Show that, for any $k > 2$, $\lim_{n \rightarrow \infty}(X_{n} \text{is divisible by k}) = \frac{1}{k}$.