Bayes’ theorem

E139495

probability theorem result in probability theory

Bayes’ theorem is a fundamental result in probability theory that describes how to update the probability of a hypothesis based on new evidence.

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All labels observed (9)

Label	Occurrences
Bayes' theorem	10
Bayes theorem	7
Bayes rule	3
Bayes’ theorem canonical	2
Bayesian probability	1
Bayesian updating rule	1
Bayes’ law	1
Bayes’ rule	1
Bayes’ theorem for continuous distributions	1

How this entity was disambiguated

This entity first appeared as the object of triple T1221712 — 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’ theorem
Context triple: [Pierre-Simon Laplace, contributedTo, Bayes’ theorem]

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. A Treatise on Probability
A Treatise on Probability is John Maynard Keynes’s influential 1921 work that develops a logical and philosophical theory of probability, challenging classical and frequency-based interpretations.
C. Logical Foundations of Probability
Logical Foundations of Probability is a seminal philosophical work by Rudolf Carnap that develops a rigorous logical and formal account of probability and inductive reasoning.
D. Occam's razor
Occam's razor is a philosophical and scientific principle that advises preferring the simplest explanation that adequately accounts for all observed facts.
E. Gaussian law of error
The Gaussian law of error is a fundamental statistical principle stating that measurement errors tend to follow a normal (bell-shaped) distribution, forming the basis of much of probability theory and statistical inference.
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’ theorem
Target entity description: Bayes’ theorem is a fundamental result in probability theory that describes how to update the probability of a hypothesis based on new evidence.

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. A Treatise on Probability
A Treatise on Probability is John Maynard Keynes’s influential 1921 work that develops a logical and philosophical theory of probability, challenging classical and frequency-based interpretations.
C. Logical Foundations of Probability
Logical Foundations of Probability is a seminal philosophical work by Rudolf Carnap that develops a rigorous logical and formal account of probability and inductive reasoning.
D. Occam's razor
Occam's razor is a philosophical and scientific principle that advises preferring the simplest explanation that adequately accounts for all observed facts.
E. Gaussian law of error
The Gaussian law of error is a fundamental statistical principle stating that measurement errors tend to follow a normal (bell-shaped) distribution, forming the basis of much of probability theory and statistical inference.
F. None of above. chosen

Statements (49)

Predicate	Object
instanceOf	probability theorem ⓘ result in probability theory ⓘ
alsoCalled	Bayes’ law ⓘ linked to: Bayes’ theorem Bayes’ rule ⓘ linked to: Bayes’ theorem
appliesTo	continuous random variables ⓘ discrete random variables ⓘ
assumes	P(B) > 0 for conditioning event B ⓘ well-defined probability space ⓘ
component	evidence probability ⓘ likelihood ⓘ posterior probability ⓘ prior probability ⓘ
contrastsWith	frequentist interpretation of probability ⓘ
coreFormula	P(A\|B) = P(B\|A) P(A) / P(B) ⓘ P(H\|E) = P(E\|H) P(H) / P(E) ⓘ
derivedFrom	definition of conditional probability ⓘ product rule of probability ⓘ
describes	updating probabilities of hypotheses given evidence ⓘ
field	Bayesian inference ⓘ probability theory ⓘ statistics ⓘ
foundationOf	Bayesian inference ⓘ
generalForm	P(A_i\|B) = P(B\|A_i) P(A_i) / Σ_j P(B\|A_j) P(A_j) ⓘ
generalizedBy	Bayes’ theorem for continuous distributions ⓘ linked to: Bayes’ theorem
hasNotation	P(H\|E) ∝ P(E\|H) P(H) ⓘ
historicalAttribution	first published posthumously by Richard Price ⓘ
implies	posterior is proportional to likelihood times prior ⓘ
mathematicalDomain	measure-theoretic probability ⓘ
namedAfter	Thomas Bayes ⓘ
relates	posterior probability to prior probability and likelihood ⓘ
timePeriod	18th century ⓘ
usedFor	computing diagnostic test accuracy ⓘ inverting conditional probabilities ⓘ learning from data ⓘ sequential updating of beliefs ⓘ
usedIn	A/B testing ⓘ Bayesian networks ⓘ Bayesian statistics ⓘ Bayesian updating ⓘ Naive Bayes classifier ⓘ decision theory ⓘ machine learning ⓘ medical diagnosis ⓘ pattern recognition ⓘ signal processing ⓘ spam filtering ⓘ
usesConcept	conditional probability ⓘ joint probability ⓘ marginal probability ⓘ

How these facts were elicited

Referenced by (27)

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

Pierre-Simon Laplace → contributedTo → Bayes’ theorem ⓘ

Bayesian inference → basedOn → Bayes' theorem ⓘ

linked to: Bayes’ theorem

Bayes’ theorem → alsoCalled → Bayes’ rule ⓘ

linked to: Bayes’ theorem

Bayes’ theorem → alsoCalled → Bayes’ law ⓘ

linked to: Bayes’ theorem

Bayes’ theorem → generalizedBy → Bayes’ theorem for continuous distributions ⓘ

linked to: Bayes’ theorem

Kalman filter → basedOn → Bayes theorem ⓘ

linked to: Bayes’ theorem

Probability theory → usesConcept → Bayes' theorem ⓘ

subject linked to: Probability Theory

linked to: Bayes’ theorem

Bayesian networks → basedOn → Bayes theorem ⓘ

linked to: Bayes’ theorem

Bayesian linear regression → basedOn → Bayes' theorem ⓘ

linked to: Bayes’ theorem

Thomas Bayes → knownFor → Bayes' theorem ⓘ

linked to: Bayes’ theorem

Thomas Bayes → hasTheoremNamedAfter → Bayes' theorem ⓘ

linked to: Bayes’ theorem

Truth and Probability → relatedTo → Bayes' theorem ⓘ

subject linked to: 1926 paper "Truth and Probability"

linked to: Bayes’ theorem

Naive Bayes classifier → basedOn → Bayes' theorem ⓘ

linked to: Bayes’ theorem

Bayesian epistemology → uses → Bayes’ theorem ⓘ

decision theory → usesConcept → Bayes rule ⓘ

linked to: Bayes’ theorem

Bayes optimality → relatedTo → Bayes rule ⓘ

linked to: Bayes’ theorem

Bayesian model averaging → basedOn → Bayes theorem ⓘ

linked to: Bayes’ theorem

An Essay towards solving a Problem in the Doctrine of Chances → mainSubject → Bayes theorem ⓘ

linked to: Bayes’ theorem

An Essay towards solving a Problem in the Doctrine of Chances → introducedConcept → Bayes theorem ⓘ

linked to: Bayes’ theorem

An Essay towards solving a Problem in the Doctrine of Chances → relatedWork → Bayes theorem ⓘ

linked to: Bayes’ theorem

Thomas Bayes → knownFor → Bayes' theorem ⓘ

subject linked to: Bayes

linked to: Bayes’ theorem

Bayes → hasNotableAssociation → Bayes' theorem ⓘ

linked to: Bayes’ theorem

Bayes → hasNotableAssociation → Bayesian probability ⓘ

linked to: Bayes’ theorem

forward-backward algorithm → basedOn → Bayes rule ⓘ

linked to: Bayes’ theorem

Calculated Risks → explainsConcept → Bayes' theorem ⓘ

linked to: Bayes’ theorem

Laplace's rule of succession → category → Bayesian updating rule ⓘ

subject linked to: Laplace's rule of succession (as a special case)

linked to: Bayes’ theorem

Bayesian learning for neural networks → usesConcept → Bayes theorem ⓘ

linked to: Bayes’ theorem

All labels observed (9)

How this entity was disambiguated Show

Statements (49)

How these facts were elicited Show

Referenced by (27)

How this entity was disambiguated

How these facts were elicited