Definition
A class of algorithms for sampling from probability distributions based on constructing a Markov chain that converges to the desired distribution.
Detailed Explanation
MCMC methods combine Markov chains with Monte Carlo sampling to generate samples from complex probability distributions. The algorithms construct a Markov chain whose stationary distribution is the target distribution of interest. Common implementations include Metropolis-Hastings and Gibbs sampling algorithms.
Use Cases
Bayesian inference, physics simulations, computational biology, financial modeling, and machine learning parameter estimation.