Markov Chain Monte Carlo

Definition

Markov Chain Monte Carlo (MCMC) is a method to sample from a distribution $\pi$ by constructing a time reversible Markov chain.

Metropolis-Hastings Algorithm

1. Propose jump from $i$ to $j$ with probability $q_{ij}$
2. Accept with probability: ${\alpha }_{ij}=\min \left(1,\frac{{\pi }_j{q}_{ji}}{{\pi }_i{q}_{ij}}\right)$

Related

• Time Reversible Markov Chain