Metropolis algorithm

E260028

Markov chain Monte Carlo method Monte Carlo method sampling algorithm stochastic algorithm

The Metropolis algorithm is a foundational Markov chain Monte Carlo method used to sample from complex probability distributions by accepting or rejecting proposed moves according to a specific probabilistic rule.

Try in SPARQL Jump to: Surface forms Disambiguation Statements Elicitation Referenced by

All labels observed (3)

Label	Occurrences
Metropolis algorithm canonical	5
Metropolis–Hastings algorithm	5
random-walk Metropolis	1

How this entity was disambiguated

This entity first appeared as the object of triple T2373449 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.

NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07

Target entity: Metropolis algorithm
Context triple: [Markov chain Monte Carlo, hasMethod, Metropolis algorithm]

A. Markov chain Monte Carlo
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.
B. Monte Carlo method
The Monte Carlo method is a computational technique that uses random sampling to approximate numerical results, especially for complex integrals, simulations, and probabilistic systems.
C. Monte Carlo
Monte Carlo is a famous district of Monaco renowned for its luxury casinos, upscale resorts, and role as a glamorous hub for high-end tourism and events like the Monaco Grand Prix.
D. Euler–Maruyama method
The Euler–Maruyama method is a basic time-stepping scheme for numerically approximating solutions to stochastic differential equations, widely used in simulations of systems with noise such as Langevin dynamics.
E. Euler’s method for numerical integration
Euler’s method for numerical integration is a simple first-order numerical procedure used to approximate solutions to ordinary differential equations by stepping forward in small increments.
F. None of above. chosen
G. Unsure - the case is ambiguous/there is not enough information to decide.

NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07

Target entity: Metropolis algorithm
Target entity description: The Metropolis algorithm is a foundational Markov chain Monte Carlo method used to sample from complex probability distributions by accepting or rejecting proposed moves according to a specific probabilistic rule.

A. Markov chain Monte Carlo
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.
B. Monte Carlo method
The Monte Carlo method is a computational technique that uses random sampling to approximate numerical results, especially for complex integrals, simulations, and probabilistic systems.
C. Monte Carlo
Monte Carlo is a famous district of Monaco renowned for its luxury casinos, upscale resorts, and role as a glamorous hub for high-end tourism and events like the Monaco Grand Prix.
D. Euler–Maruyama method
The Euler–Maruyama method is a basic time-stepping scheme for numerically approximating solutions to stochastic differential equations, widely used in simulations of systems with noise such as Langevin dynamics.
E. Euler’s method for numerical integration
Euler’s method for numerical integration is a simple first-order numerical procedure used to approximate solutions to ordinary differential equations by stepping forward in small increments.
F. None of above. chosen

Statements (50)

Predicate	Object
instanceOf	Markov chain Monte Carlo method ⓘ Monte Carlo method ⓘ sampling algorithm ⓘ stochastic algorithm ⓘ
acceptanceProbabilityForSymmetricProposal	min(1, π(x') / π(x)) ⓘ
aimsTo	sample from target probability distribution ⓘ
appliedIn	Bayesian inference ⓘ Ising model simulations ⓘ computational biology ⓘ image analysis ⓘ lattice field theory ⓘ machine learning ⓘ spin systems ⓘ
basedOn	detailed balance condition ⓘ ergodicity of Markov chains ⓘ
category	numerical method in probability theory ⓘ randomized algorithm ⓘ
coDevelopedBy	Arianna W. Rosenbluth ⓘ Augusta H. Teller ⓘ Edward Teller ⓘ Marshall N. Rosenbluth ⓘ
convergesTo	target distribution under regularity conditions ⓘ
field	Bayesian statistics ⓘ computational chemistry ⓘ computational physics ⓘ statistical mechanics ⓘ statistics ⓘ
generalizedBy	Metropolis algorithm self-linksurface differs ⓘ surface form: Metropolis–Hastings algorithm
hasProperty	accepts or rejects proposed moves probabilistically ⓘ can be used with symmetric proposal distributions ⓘ constructs reversible Markov chain ⓘ does not require normalization constant of target distribution ⓘ generates samples asymptotically from target distribution ⓘ
introducedIn	1953 ⓘ
namedAfter	Nicholas Metropolis ⓘ
publishedIn	Journal of Chemical Physics ⓘ
relatedTo	Gibbs sampling ⓘ Hamiltonian Monte Carlo ⓘ importance sampling ⓘ simulated annealing ⓘ
step	accept proposed state with acceptance probability ⓘ compute acceptance probability ⓘ otherwise retain current state ⓘ propose new state from proposal distribution ⓘ
titleOfOriginalPaper	Equation of State Calculations by Fast Computing Machines ⓘ
uses	Markov processes ⓘ surface form: Markov chain acceptance–rejection rule ⓘ proposal distribution ⓘ stationary distribution ⓘ
yearOfFirstUse	1953 ⓘ