Markov chain Monte Carlo

E46140

Monte Carlo method computational algorithm sampling algorithm stochastic simulation method

Markov chain Monte Carlo is a class of algorithms that uses Markov chains to generate samples from complex probability distributions, widely used in Bayesian inference, statistical physics, and machine learning.

Observed surface forms (4)

Surface form	Occurrences
Hamiltonian Monte Carlo	1
Metropolis-Hastings algorithm	1
Monte Carlo method	1
random-walk Metropolis	1

Statements (68)

Predicate	Object
instanceOf	Monte Carlo method ⓘ computational algorithm ⓘ sampling algorithm ⓘ stochastic simulation method ⓘ
aimsTo	generate samples from a target probability distribution ⓘ
applicationDomain	Bayesian inference ⓘ computational biology ⓘ econometrics ⓘ graphical models ⓘ machine learning ⓘ spatial statistics ⓘ statistical physics ⓘ
basedOn	Markov processes ⓘ surface form: Markov property Monte Carlo method ⓘ surface form: Monte Carlo integration
canBe	multiple-chain ⓘ single-chain ⓘ
hasChallenge	diagnosing convergence ⓘ multimodal target distributions ⓘ slow mixing in high dimensions ⓘ
hasImprovement	adaptive proposals ⓘ gradient-based proposals ⓘ parallel tempering ⓘ
hasKeyConcept	Markov chain state space ⓘ acceptance probability ⓘ autocorrelation ⓘ burn-in period ⓘ convergence diagnostics ⓘ detailed balance ⓘ ergodicity ⓘ mixing time ⓘ proposal distribution ⓘ stationary distribution ⓘ transition kernel ⓘ
hasMethod	Gibbs sampling ⓘ Hamiltonian Monte Carlo ⓘ Metropolis algorithm ⓘ Langevin dynamics ⓘ surface form: Metropolis-adjusted Langevin algorithm Metropolis algorithm ⓘ surface form: Metropolis–Hastings algorithm adaptive MCMC ⓘ blocked Gibbs sampling ⓘ independence sampler ⓘ Markov chain Monte Carlo self-linksurface differs ⓘ surface form: random-walk Metropolis reversible jump MCMC ⓘ slice sampling ⓘ
originatedInField	statistical physics ⓘ
property	asymptotically exact under regularity conditions ⓘ produces correlated samples ⓘ requires convergence to stationary distribution ⓘ
relatedTo	importance sampling ⓘ sequential Monte Carlo ⓘ variational inference ⓘ
requires	aperiodic Markov chain ⓘ irreducible Markov chain ⓘ positive recurrent Markov chain ⓘ
typicallyTargets	complex probability distributions ⓘ high-dimensional probability distributions ⓘ
usedFor	Bayesian model comparison ⓘ Boltzmann distribution sampling ⓘ Ising model simulation ⓘ approximating posterior distributions ⓘ estimating integrals ⓘ parameter estimation ⓘ simulating physical systems at equilibrium ⓘ uncertainty quantification ⓘ
uses	Markov processes ⓘ surface form: Markov chain
widelyUsedIn	Bayesian statistics ⓘ deep generative modeling ⓘ probabilistic programming ⓘ

Referenced by (8)

Full triples — surface form annotated when it differs from this entity's canonical label.

Markov chain Monte Carlo → hasMethod → Markov chain Monte Carlo self-linksurface differs ⓘ

this entity surface form: random-walk Metropolis

Boltzmann machines → hasSamplingMethod → Markov chain Monte Carlo ⓘ

Monte Carlo method → includes → Markov chain Monte Carlo ⓘ

Stanislaw Ulam → notableWork → Markov chain Monte Carlo ⓘ

this entity surface form: Monte Carlo method

Yee-Whye Teh → researchInterest → Markov chain Monte Carlo ⓘ

Bayesian inference → uses → Markov chain Monte Carlo ⓘ

this entity surface form: Metropolis-Hastings algorithm

Bayesian inference → uses → Markov chain Monte Carlo ⓘ

this entity surface form: Hamiltonian Monte Carlo