Bayes factor

E700155

Bayesian model comparison metric likelihood ratio statistical measure

The Bayes factor is a Bayesian model comparison metric that quantifies how much more strongly data support one statistical model or hypothesis over another.

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

All labels observed (3)

Label	Occurrences
Bayes factor canonical	1
Bayesian evidence ratio	1
Bayesian marginal likelihood	1

How this entity was disambiguated

This entity first appeared as the object of triple T7906458 — 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: Bayes factor
Context triple: [Bayesian Occam factor, relatedTo, Bayes factor]

A. 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.
B. Bayes’ theorem
Bayes’ theorem is a fundamental result in probability theory that describes how to update the probability of a hypothesis based on new evidence.
C. Bayesian Occam factor
The Bayesian Occam factor is a term in Bayesian model comparison that automatically penalizes overly complex models by integrating over their larger parameter spaces, thereby implementing Occam’s razor in probabilistic inference.
D. Bayesian networks
Bayesian networks are probabilistic graphical models that represent variables and their conditional dependencies using directed acyclic graphs, enabling structured reasoning and inference under uncertainty.
E. 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.
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: Bayes factor
Target entity description: The Bayes factor is a Bayesian model comparison metric that quantifies how much more strongly data support one statistical model or hypothesis over another.

A. 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.
B. Bayes’ theorem
Bayes’ theorem is a fundamental result in probability theory that describes how to update the probability of a hypothesis based on new evidence.
C. Bayesian Occam factor
The Bayesian Occam factor is a term in Bayesian model comparison that automatically penalizes overly complex models by integrating over their larger parameter spaces, thereby implementing Occam’s razor in probabilistic inference.
D. Bayesian networks
Bayesian networks are probabilistic graphical models that represent variables and their conditional dependencies using directed acyclic graphs, enabling structured reasoning and inference under uncertainty.
E. 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.
F. None of above. chosen

Statements (48)

Predicate	Object
instanceOf	Bayesian model comparison metric ⓘ likelihood ratio ⓘ statistical measure ⓘ
alternativeName	Bayesian evidence ratio ⓘ linked to: Bayes factor
appliedIn	biostatistics ⓘ econometrics ⓘ machine learning ⓘ physics ⓘ psychology ⓘ
approximatedBy	BIC difference ⓘ
compares	two hypotheses ⓘ two statistical models ⓘ
computedBy	Laplace approximation ⓘ linked to: Laplace method Monte Carlo methods ⓘ bridge sampling ⓘ reversible jump MCMC ⓘ
contrastsWith	frequentist hypothesis tests ⓘ p-values ⓘ
definedAs	ratio of marginal likelihoods of two models ⓘ
dependsOn	likelihood function ⓘ prior distributions ⓘ
domain	statistical inference ⓘ
hasFormula	B_10 = p(y \| M_1) / p(y \| M_0) ⓘ
hasProperty	can accumulate evidence for the null model ⓘ can be computed analytically in simple models ⓘ often requires numerical integration ⓘ penalizes model complexity via marginalization ⓘ sensitive to prior specification ⓘ
interpretedAs	how much data update prior odds to posterior odds ⓘ
interpretedUsing	Jeffreys scale ⓘ linked to: Jeffreys scale for Bayes factors Kass and Raftery scale ⓘ
introducedBy	Harold Jeffreys ⓘ
invariantUnder	reparameterization of model parameters ⓘ
measures	strength of evidence in data for one model over another ⓘ
quantifies	relative evidence from data ⓘ
relatedTo	Bayesian Information Criterion ⓘ marginal likelihood ⓘ posterior odds ⓘ prior odds ⓘ
symbol	B_10 ⓘ K ⓘ
usedFor	hypothesis testing ⓘ model comparison ⓘ
usedIn	Bayesian statistics ⓘ linked to: Bayesian inference
usedTo	assess evidence for alternative hypothesis ⓘ assess evidence for null hypothesis ⓘ select between nested models ⓘ select between non-nested models ⓘ

How these facts were elicited

Referenced by (3)

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

Bayesian Occam factor → relatedTo → Bayes factor ⓘ

Bayes factor → alternativeName → Bayesian evidence ratio ⓘ

linked to: Bayes factor

minimum description length principle → comparedTo → Bayesian marginal likelihood ⓘ