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.

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All labels observed (6)

Label	Occurrences
Markov chain Monte Carlo canonical	11
Hamiltonian Monte Carlo	1
Markov chain Monte Carlo methods	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 (16)

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

Boltzmann machines → hasSamplingMethod → Markov chain Monte Carlo ⓘ

Stanislaw Ulam → notableWork → Markov chain Monte Carlo ⓘ

this entity surface form: Monte Carlo method

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

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

this entity surface form: random-walk Metropolis

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

Monte Carlo method → includes → Markov chain Monte Carlo ⓘ

Nick Metropolis → influenced → Markov chain Monte Carlo ⓘ

this entity surface form: Markov chain Monte Carlo methods

Nick Metropolis → usedIn → Markov chain Monte Carlo ⓘ

subject surface form: Metropolis algorithm

Bayesian networks → inferenceAlgorithms → Markov chain Monte Carlo ⓘ

Bayesian linear regression → canBeEstimatedBy → Markov chain Monte Carlo ⓘ

Markov random fields → inferenceMethodsInclude → Markov chain Monte Carlo ⓘ

subject surface form: Markov random field

Probabilistic Graphical Models: Principles and Techniques → topic → Markov chain Monte Carlo ⓘ

Dirichlet process models → inferenceMethod → Markov chain Monte Carlo ⓘ

Radford M. Neal → fieldOfWork → Markov chain Monte Carlo ⓘ