Hamiltonian Monte Carlo

E260030

Bayesian computation method Markov chain Monte Carlo algorithm Monte Carlo method sampling algorithm

Hamiltonian Monte Carlo is an advanced Markov chain Monte Carlo sampling algorithm that uses concepts from Hamiltonian dynamics to efficiently explore complex, high-dimensional probability distributions.

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All labels observed (3)

Label	Occurrences
Hamiltonian Monte Carlo canonical	3
Hybrid Monte Carlo	1
Riemannian Manifold Hamiltonian Monte Carlo	1

How this entity was disambiguated

This entity first appeared as the object of triple T2373452 — 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: Hamiltonian Monte Carlo
Context triple: [Markov chain Monte Carlo, hasMethod, Hamiltonian Monte Carlo]

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. Adam: A Method for Stochastic Optimization
"Adam: A Method for Stochastic Optimization" is a highly influential machine learning paper that introduces the Adam optimizer, a widely used adaptive gradient-based optimization algorithm for training deep neural networks.
C. Boltzmann machines
Boltzmann machines are stochastic recurrent neural networks used for learning complex probability distributions, foundational in unsupervised learning and energy-based models.
D. Bayesian linear regression
Bayesian linear regression is a statistical modeling approach that treats regression coefficients and predictions probabilistically by placing prior distributions on parameters and updating them with observed data.
E. Bayesian inference
Bayesian inference is a statistical framework that updates the probability of hypotheses as more evidence or data becomes available, using Bayes’ theorem to combine prior beliefs with observed information.
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: Hamiltonian Monte Carlo
Target entity description: Hamiltonian Monte Carlo is an advanced Markov chain Monte Carlo sampling algorithm that uses concepts from Hamiltonian dynamics to efficiently explore complex, high-dimensional probability distributions.

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. Adam: A Method for Stochastic Optimization
"Adam: A Method for Stochastic Optimization" is a highly influential machine learning paper that introduces the Adam optimizer, a widely used adaptive gradient-based optimization algorithm for training deep neural networks.
C. Boltzmann machines
Boltzmann machines are stochastic recurrent neural networks used for learning complex probability distributions, foundational in unsupervised learning and energy-based models.
D. Bayesian linear regression
Bayesian linear regression is a statistical modeling approach that treats regression coefficients and predictions probabilistically by placing prior distributions on parameters and updating them with observed data.
E. Bayesian inference
Bayesian inference is a statistical framework that updates the probability of hypotheses as more evidence or data becomes available, using Bayes’ theorem to combine prior beliefs with observed information.
F. None of above. chosen

Statements (51)

Predicate	Object
instanceOf	Bayesian computation method ⓘ Markov chain Monte Carlo algorithm ⓘ Monte Carlo method ⓘ sampling algorithm ⓘ
advantageOver	Metropolis–Hastings with local proposals ⓘ random-walk Metropolis ⓘ linked to: Metropolis algorithm
aimsTo	efficiently explore complex probability distributions ⓘ efficiently explore high-dimensional probability distributions ⓘ
alsoKnownAs	Hybrid Monte Carlo ⓘ linked to: Hamiltonian Monte Carlo
assumes	continuous parameter space ⓘ
basedOn	Hamiltonian function ⓘ linked to: Hamiltonian (time translation generator) Hamiltonian system ⓘ linked to: Hamiltonian mechanics
benefit	better mixing in high dimensions ⓘ lower autocorrelation between samples ⓘ more efficient exploration of posterior geometry ⓘ reduced random walk behavior ⓘ
generalization	No-U-Turn Sampler ⓘ Riemannian Manifold Hamiltonian Monte Carlo ⓘ linked to: Hamiltonian Monte Carlo
hasHyperparameter	mass matrix ⓘ number of leapfrog steps ⓘ step size ⓘ
implementedIn	NumPyro ⓘ PyMC ⓘ linked to: PyMC3 Stan ⓘ TensorFlow Probability ⓘ linked to: TensorFlow Probability (JAX backend)
introducedBy	Radford M. Neal ⓘ
introducesAuxiliaryVariable	momentum ⓘ
keyProperty	approximate energy conservation ⓘ reversibility ⓘ volume preservation ⓘ
limitation	less suitable for discrete parameters ⓘ requires gradient computations ⓘ
modelsStateWith	momentum variables ⓘ position variables ⓘ
requires	differentiable target density ⓘ gradient of log target density ⓘ
targetDistribution	posterior distribution ⓘ probability density ⓘ
typicalApplication	posterior inference in complex models ⓘ
typicallyUses	leapfrog integrator ⓘ symplectic integrator ⓘ
usedIn	Bayesian hierarchical models ⓘ Bayesian machine learning ⓘ Bayesian statistics ⓘ linked to: Bayesian inference computational biology ⓘ computational physics ⓘ
usesConceptsFrom	Hamiltonian dynamics ⓘ classical mechanics ⓘ
usesTransitionKernel	Metropolis acceptance step ⓘ deterministic Hamiltonian dynamics ⓘ
yearOfEarlyDevelopment	late 1980s ⓘ

How these facts were elicited

Referenced by (5)

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

Markov chain Monte Carlo → hasMethod → Hamiltonian Monte Carlo ⓘ

Metropolis algorithm → relatedTo → Hamiltonian Monte Carlo ⓘ

Gibbs sampling → relatedTo → Hamiltonian Monte Carlo ⓘ

Hamiltonian Monte Carlo → generalization → Riemannian Manifold Hamiltonian Monte Carlo ⓘ

linked to: Hamiltonian Monte Carlo

Hamiltonian Monte Carlo → alsoKnownAs → Hybrid Monte Carlo ⓘ