Overview
MCMC methods are used to sample from complex, high-dimensional probability distributions where direct sampling is difficult. They are a cornerstone of modern Bayesian statistics.
How it Works
- Markov Chain: A sequence of random variables where the next state depends only on the current state.
- Monte Carlo: Using random sampling to estimate properties of the distribution.
By constructing a Markov chain that has the desired distribution as its equilibrium distribution, one can obtain samples from that distribution by running the chain for a long time.
Popular Algorithms
- Metropolis-Hastings
- Gibbs Sampling