Markov Chain Monte Carlo
Markov Chain Monte Carlo (MCMC) is a computational methodology used for sampling from complex probability distributions, particularly in Bayesian statistics and machine learning. It combines Markov chains, which model sequences of random variables with memoryless transitions, with Monte Carlo methods, which rely on random sampling to approximate numerical results. MCMC enables inference in models where direct analytical solutions are intractable, such as estimating posterior distributions in high-dimensional spaces.
Developers should learn MCMC when working on probabilistic models, Bayesian inference, or simulations in fields like data science, finance, or physics, where exact calculations are infeasible. It is essential for tasks like parameter estimation, uncertainty quantification, and generative modeling, as it allows sampling from distributions that cannot be derived analytically. For example, in machine learning, MCMC is used in Bayesian neural networks or topic modeling with Latent Dirichlet Allocation (LDA).